EXHIBIT 10.6

ATWOOD OCEANICS, INC

AMENDED AND RESTATED

2007 NONEMPLOYEE DIRECTORS’ ELECTIVE DEFERRED COMPENSATION PLAN

(as amended and restated effective March 7, 2013)

1. Purpose.

The purpose of this Plan is to provide nonemployee directors of the Corporation with an opportunity to defer compensation earned as a director.

2. Effective Date.

This Plan shall become effective on the Effective Date.

3. Definitions.

In this Plan, the following definitions apply:

“LTIP” means the Atwood Oceanics, Inc. 2007 Long-Term Incentive Plan and the Atwood Oceanics, Inc. 2013 Long-Term Incentive Plan.

“Account” means the account maintained by the Corporation for a participant’s deferred compensation and Plan earnings.

“Administrator” means the Secretary of the Corporation.

“Board” means the Board of Directors of the Corporation.

“Compensation” means the cash retainer payable to a nonemployee director annually in January for service on the Board during the calendar year, and restricted stock awards to nonemployee directors. Cash fees other than the annual cash retainer, grants of stock options, and reimbursement of expenses do not constitute compensation for purposes of the Plan. Compensation is “for” a particular calendar year if the services for which it is to be paid are performed or to be performed in that calendar year.

“Corporation” means Atwood Oceanics, Inc., a Texas corporation, and its successors.

“Deferred cash” means a credit to a participant’s account under Section 6(b) that represents the right to (i) receive a cash payment equal to the credited amount and (ii) have deemed interest determined under Section 6(b) credited to the account.

“Deferred stock unit” means a credit to a participant’s account under Section 6(c) that represents the right to (i) receive a payment of cash or stock equal to the credited amount

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and (ii) have Plan earnings determined as dividends or other distributions determined under Section 6(c) credited to the account.

“Effective date” means December 1, 2007.

“Fair market value” means, for any date, the average of the high and low sales prices for shares as reported on the Consolidated Tape during the New York Stock Exchange regular session on such date.

“Nonemployee director” means a member of the Board who is not also an employee of the Corporation or any affiliate of the Corporation.

“Participant” means each nonemployee director who has elected to defer compensation under this Plan and has not yet received full payment of his or her account.

“Plan” means this Atwood Oceanics, Inc. 2007 Nonemployee Directors’ Elective Deferred Compensation Plan, as it may be amended from time to time.

“Plan Earnings” means notional interest as determined under Section 6(b) or notional dividends or other distributions with respect to shares as determined under Section 6(c).

“Rabbi Trust” means a grantor trust funded by the Corporation to which the Corporation makes contributions and which is obligated to pay all or a portion of the Plan’s benefits, to the extent the Corporation does not pay them directly. A rabbi trust will generally provide that except in the case of the Corporation’s bankruptcy or other insolvency, the Corporation has no right to withdraw assets from the rabbi trust or to require the trustee of the rabbi trust to stop payments to a participant or beneficiary. However, a rabbi trust will provide that in the event of the Corporation’s bankruptcy or other insolvency, the trustee will stop any payments from the rabbi trust to participants or beneficiaries and will hold the assets of the rabbi trust for the benefit of the Corporation’s creditors, including participants and beneficiaries owed amounts under the Plan, but also including all other general unsecured creditors of the Corporation. Any rabbi trust shall hold all of its assets in the United States.

“Restricted stock award” means an award of restricted stock units granted to a nonemployee director under the LTIP.

“Share” means a share of common stock of the Corporation.

“Unforeseeable emergency” means a severe financial hardship of the participant resulting from an illness or accident of the participant or of the participant’s spouse or dependent (as defined in Internal Revenue Code Section 152(a)) loss of the participant’s property due to casualty, or other similar extraordinary and unforeseeable circumstances arising as a result of events beyond the control of the participant.

4. Administration.

(a) Authority of Administrator. The Board and, the subject to the oversight of the Board, the Administrator shall have authority to administer the Plan, including conclusive authority to construe and interpret the Plan, to establish rules, policies, procedures,

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forms, and notices for use in carrying out the Plan, and to make all other determinations necessary or desirable for administration of the Plan.

(b) Indemnity of Administrator and Board Members.

(1) The Corporation (the “Indemnifying Party”) hereby agrees to indemnify and hold harmless the Administrator and members of the Board (the “Indemnified Parties”) against any losses, claims, damages, or liabilities to which any of the Indemnified Parties may become subject to the extent that such losses, claims, damages, liabilities, or actions in respect thereof arise out of or are based upon any act or omission of such Indemnified Party in connection with the administration of this Plan (including any act or omission constituting negligence on the part of such Indemnified Party, but excluding any act or omission constituting gross negligence or willful misconduct on the part of such Indemnified Party), and will reimburse the Indemnified Party for any legal or other expenses reasonably incurred by him or her in connection with investigating or defending against any such loss, claim, damage, liability, or action.

(2) Promptly after receipt by the Indemnified Party under clause (1) above of notice of the commencement of any action or proceeding with respect to any loss, claim, damage, or liability against which the Indemnified Party believes he or she is indemnified under clause (1) above, the Indemnified Party shall, if a claim with respect thereto is to be made against the Indemnifying Party under such Section, notify the Indemnifying Party in writing of the commencement thereof; provided, however, that the omission so to notify the Indemnifying Party shall not relieve it from any liability which it may have to the Indemnified Party to the extent the Indemnifying Party is not prejudiced by such omission. If any such action or proceeding shall be brought against the Indemnified Party and it shall notify the Indemnifying Party of the commencement thereof, the Indemnifying Party shall be entitled to participate therein, and, to the extent that it shall wish, to assume the defense thereof, with counsel reasonably satisfactory to the Indemnified Party, and, after notice from the Indemnifying Party to the Indemnified Party of its election to assume the defense thereof, the Indemnifying Party shall not be liable to such Indemnified Party under clause (1) above for any legal or other expenses subsequently incurred by the Indemnified Party in connection with the defense thereof other than reasonable costs of investigation or reasonable expenses of actions taken at the written request of the Indemnifying Party. The Indemnifying Party shall not be liable for any compromise or settlement of any such action or proceeding affected without its consent, which consent will not be unreasonably withheld.

5.    Election to Defer Compensation

a) Amount of Deferral. Any nonemployee director may elect to defer receipt of all or a specified percentage of the compensation otherwise payable to such director.

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b) Manner of Electing Deferral. An election to defer compensation shall be made by giving written notice to the Administrator in the form approved by the Administrator. Such notice shall include:

(1) The percentage of compensation to be deferred; and

(2) Unless the default payment date is to apply, the date of payment of the compensation deferred for the calendar year and all Plan earnings attributable to such compensation.

c)Time of Election: Election Changes.

(1) An election to defer compensation other than a restricted stock award must be made by a nonemployee director on or before December 31 of the calendar year preceding the calendar year for which the compensation would otherwise be payable.

(2) An election to defer all or a portion of a restricted stock award must be made by a nonemployee director no later than the earlier of:

(A) 30 days after the date of grant of the restricted stock award; or

(B) the date that is 12 months before the restricted stock award’s scheduled vesting date.

(3) An election shall continue in effect until changed as provided in clause (4) below.

(4) A non-employee director may at any time change a deferral election by giving written notice to the Administrator in the form approved by the Administrator, provided that, except in the case of a restricted stock award, no change may be effective for compensation for the calendar year in which the Administrator receives such notice or for compensation for any earlier calendar year, and in case of a restricted stock award no change may be effective after the last date on which the nonemployee director could elect to defer all or part of the restricted stock award.

(5) Notwithstanding clauses (1) and (4) above, a non-employee director upon first being elected to the Board may make an election to defter compensation other than a restricted stock award at any time within 30 days after his or her first being elected to the Board, but such election shall not apply to compensation earned before the date on which it is made.

6.    Deferred Compensation Account

(a) Establishment of Account. The Corporation will maintain an account for each participant. Except to the extent of any rabbi trust (which the corporation may, but is not required to, establish), accounts under this Plan shall be unfunded and shall represent only an unsecured claim against the general assets of the Corporation.

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For purposes of determining when payment must be made or is due, separate subaccounts shall be maintained in each participant’s account for compensation and restricted stock awards deferred for each calendar year and all Plan earnings attributable to such compensation. Such subaccounts shall further be subdivided into the portion credited with deferred cash and the portion credited with deferred stock units.

(b) Deferred Cash. To the extent that a participant elects to defer compensation other than a restricted stock award, the amount so deferred will be credited as deferred cash to the participant’s account as of the date such compensation would otherwise have been payable absent the election to defer. Thereafter, at the end of each calendar quarter, deferred cash credits in the account shall be increased by an amount equal to deemed interest upon the average daily balance of deferred cash in the account during such quarter. The rate of interest used to determine such deemed interest as of any date shall be the monthly rate determined based on the rate reported on such date as the current annual “prime rate” in the “Bonds Rates & Yields” section, or any successor to such section, of the Wall Street Journal.

(c) Deferred Stock Units.

(1) To the extent that a participant elects to defer all or a portion of a restricted stock award, a number of deferred stock units will be credited to the participant’s account equal to the number of shares of stock covered by the restricted stock award, or by the portion of the restricted stock award that the participant elects to defer under the Plan, as soon as administratively feasible following the date after which the participant’s election to defer all or a portion of the restricted stock award become irrevocable. If, after the date of the crediting to the participant’s account of any deferred stock units attributable to a restricted stock award, the restricted stock award to which the deferred stock units are attributable would, under the terms of the LTIP, be forfeited because the participant fails to meet the vesting condition applicable to such award, then the deferred stock units attributable to such restricted stock award shall be forfeited under the Plan, and the number of such deferred stock units shall be debited form the participant’s Plan account. In addition, on each date on which a cash dividend or other distribution of cash or property (other than a distribution payable in the form of shares) is payable on the shares, the participant’s account shall be credited with a number of deferred stock units equal to (i) the per share amount of the cash dividend or other distribution times the number of deferred stock units then credited to the account, divided by (ii) the fair market value of a share on the last trading day preceding the dividend payment date. Accounts shall be credited with fractional deferred stock units, rounded to the third decimal place.

(2) In case of a stock split, stock dividend, or other relevant change in capitalization, the number of deferred stock units credited to a participant’s account shall be adjusted in such manner as the Administrator deems appropriate.

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(3) Notwithstanding Clauses (1) and (2) above, until the end of any “Restriction Period” that would have applied under the LTIP to a restricted stock award to which deferred stock units credited to a participant’s account are attributable, cash dividends and other distributions of cash or property payable in shares shall result in an increase in the number of deferred stock units credited to the participant’s account, and adjustments for stock splits, stock dividends, and other relevant changes shall be made to the number of deferred stock units credited to a participant’s account, only to the same extent as such increases or adjustments would have occurred to the number of shares covered by the deferred stock award to which the deferred stock units are attributable if the participant had not elected to defer all or a part of such restricted stock award.

7. Valuation

The value of an account as of any payment or other valuation date shall be the sum of (a) the amount of deferred cash then credited to the account, with deemed interest credited in accordance with Section 6(b) and prorated for the number of days in the calendar month preceding the valuation date, plus (b) an amount equal to the number of deferred stock units then credited to the account times the fair market value of a share on the last trading day preceding the valuation date.

8. Payment

(a) Separate Payment Dates for Amounts Attributable to Each Separate Calendar Year for Which Compensation Was Deferred. The date of payment shall be determined separately for each portion of the participant’s account attributable to compensation or restricted stock awards deferred for a different calendar year.

(b) Time and Manner of Payment. Payment of the amount attributable to compensation or restricted stock awards deferred for any particular calendar year shall be made in cash; provided, however, that any portion of the participant’s account credited with deferred stock units (other than any deferred stock unit representing a fractional share) may, upon the Participant’s written election, be paid in the form of shares equal in number to such deferred stock units. Such payment shall be made on the date elected by the participant or, in default of any election by the participant, on the default payment date specified in Subsection (d) or (e) below; provided, however, that no participant may elect to receive payment form the Plan of the portion if the participant’s account attributable to a particular calendar year other than as either a single lump sum or substantially equal (as determined by the Administrator in good faith) annual installments over a period not exceeding 5 years, and provided moreover that in the case of the portion of the participant’s account credited with deferred stock units, no such payment date may be before the later of the date on which the restricted stock award to which the deferred stock units are attributable becomes vested or the end of the Restriction Period applicable to such restricted stock award. If a participant elects to receive installment payments, the remaining unpaid portion of his or her account shall continue to be credited with Plan earnings.

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(c) Payment Election Changes. A participant may change or revoke his or her election with respect to the portion of his or her account attributable to compensation or a restricted stock award for a particular calendar year, or make a new election to replace a default payment date, provided that:

(1) The Administrator is provided by the participant with written notice of the change in a form approved by the Administrator;

(2) The change, revocation, or new election may have the effect of causing any amount to be paid before the date when it would otherwise have been paid under the previously elected or default date;

(3) The change must either cause (i) a previously scheduled lump sum to paid at least five years later than it otherwise would have been, or not to be paid as a lump sum, but in the form of installment payments commencing five years after the lump sum would have been paid, or (ii) previously scheduled installment payments to commence at least five years later than they otherwise would have commenced, or not to be paid as installment payments, but in the form of a lump sum payable at least five years after the first installment payment would have been paid; and

(4) No change, revocation, or new election shall be effective if the date on which payment would, but for the change, revocation, or new election, have been due occurs before the date that is one year after the date on which written notice of the change or new election is received by the Administrator.

(d) Default Time and Manner of Payment. Unless a participant elects a different form and date of payment, the portion of the participant’s account attributable to each particular calendar year shall be distributed in a single lump sum as soon as administratively feasible after his or her termination of service as a director of the Corporation.

(e) Payment on Death. Unless a participant has specifically elected otherwise, notwithstanding a participant’s election(s) as to the time or form of payment of his or her account, in the event of a participant’s death an amount of cash equal to the remaining value of the participant’s account shall be paid in a single payment to the participant’s estate or permitted designated beneficiary as soon as practicable.

(f) Unforeseeable Emergency. The Corporation may, upon a participant’s written application, pay to the participant all or any portion of the participant’s account if the Corporation determines that the participant is experiencing an unforeseeable emergency that permits making such payment without risking the Plan’s intended tax consequences; provided, however, that no portion of the participant’s account consisting of deferred stock units may be withdrawn before the later of the date on which the restricted stock award to which such deferred stock units are attributable becomes vested or the end of the restriction period with respect to such restricted stock award. The amount that the Corporation permits a participant to withdraw due to unforeseeable emergency will not exceed the amount that the Corporation determines is necessary for the participant to cope with the unforeseeable

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emergency, including, to the extent permitted in Treasury regulations and IRS rulings, taxes reasonably anticipated as a result of the withdrawal. If the Corporation permits a participant to withdraw an amount from his or her account due to unforeseeable emergency, and deferred compensation election for the calendar year in which the withdrawals permitted will be deemed to have been revoked by the participant for the remaining balance of the calendar year.

(g) No Other Withdrawals. No withdrawal may be made from a participant’s account except as provided in this Section 8.

(h) Six Month Delay for “Specified Employees”. The Administrator shall delay any payment otherwise due to a participant who is a “specified employee” under Internal Revenue Code Section 409A in connection with such participant’s termination of service that would otherwise be paid earlier than six months after the date on which the participant terminated service to a date six months after the date on which the participant terminated service.

9. Beneficiary Designation

(a) Participants may designate beneficiaries. Participants may designate a beneficiary to be paid any amounts remaining unpaid under this Plan on the death of the participant, provided that such designation will only be given effect if the designation is expressly authorized as a nontestamentary transfer under applicable laws of descent and distribution as determined by the Administrator.

(b) Beneficiary Designation Procedures. Beneficiary designations shall be subject to such forms, requirements, and procedures as the Administrator may establish from time to time.

10. Nonassignability

Except as may be required by law, the right of a participant or beneficiary to receive any unpaid portion of the participant’s account may not be anticipated, alienated, sold, transferred, or assigned except by will or the laws of descent and distribution (including permitted beneficiary designations under Section 9), and may not be pledged or encumbered, or be subject to encumbrance, attachment, garnishment, execution, or levy of any kind.

11. Amendment and Termination

This Plan may be amended, modified or terminated by the Board at any time, provided that no such amendment, modification or termination shall, without the consent of a participant, adversely affect such participant’s rights with respect to amounts accrued in the participant’s account.

12. Governing Law

This Plan and all actions taken under it shall be governed by the laws of the State of Texas, without reference to conflict of law principles.

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13. Severability

If any provisions of this Plan shall be deemed illegal or invalid for any reason, such illegality or invalidity shall not affect the remaining provisions of the Plan but shall be fully severable.

14. Tax and Other Legal Compliance

The Administrator shall administer the Plan in a manner consistent with the Corporation’s intent that amounts under the Plan not be subject to the tax or “interest” charge imposed by the Internal Revenue Code Section 409A. The Administrator is also authorized to take such steps as may be necessary including, without limitation, delaying the effectiveness of a participant’s election or delaying settlement of an account, in order to ensure that this Plan and all actions taken under it comply with any law, regulation, or listing requirement that the Administrator deems applicable or desirable, including the exemption provided by Rule 16b-3 under the Securities Exchange Act of 1934.

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