Exhibit 4.35

To: Team-Up Owning Company Limited

Trust Company Complex

Ajeltake Road

Ajeltake Island

Majuro

Marshall Islands MH96960

Orpheus Owning Company Limited

Trust Company Complex

Ajeltake Road

Ajeltake Island

Majuro

Marshall Islands MH96960

and

DryShips Inc.

Trust Company Complex

Ajeltake Road

Ajeltake Island

Majuro

Marshall Islands MH96960

19 May 2009

Dear Sirs

US$101,50,000 loan facility to Team-Up Owning Company Limited and Orpheus Owning Company Limited

We refer to the facility agreement dated 4 December 2007 in connection with the above facility (the “Facility Agreement”). Words and expressions defined therein shall, unless the context otherwise requires or unless otherwise defined herein, have the same meanings when used in this letter.

Following our discussions arid subject to documentation satisfactory in all respects to ourselves and our legal counsel, we confirm our agreement to the following arrangements in connection with the Facility Agreement and the Security Documents:

1 the, Banks will waive the application of clause 5.3 of the Corporate Guarantee for the period of twenty four (24) months commencing on the date of this letter (the “Waiver Period”);

2 the Banks will waive the application of clause 8,2.1 of the Facility Agreement for the Waiver Period:

3 the Borrowers shall not declare or pay any dividend to the Corporate Guarantor at any time until payment of all moneys payable under the Security Documents, to the effect that any surplus Earnings (as such term is defined in the relevant Ship Security Documents) will remain in the relevant Operating Account for each Ship;

4 a quarterly excess earnings recapture mechanism will be incorporated in the Facility Agreement providing that funds in excess of US$3,500,000 per Operating Account standing to the credit of each Operating Account for the relevant Ship as at the end of each quarter shall be applied quarterly in prepayment of the Loan. Such prepayment shall reduce pro rata all quarterly repayment instalments under clause 4.1 of the Facility Agreement falling due on or after 23 July 2012;

DnBNOR Bank ASA 20 St. Dunstan’s Hill, London EC3R 8HY

Tel: 020 7621 1111 Fax: 020 7626 7400 www.dnbnor.no

DnBNOR Bank ASA Incorporated in Norway with Limited Liability. Registration No: 984851006. Head Office: 0021 Osio, Norway

DnB NOR Bank ASA London Branch Registration in UK F0025119

5 the Margin will be increased to two point five zero per cent (2.50%) per annum at all times during the period commencing on 19 May 2009 and terminating upon payment of all moneys payable under the Security Documents, but to be reduced to two per cent (2%) per annum for as long as the Security Value exceeds 125% of the aggregate of (a) the Loan and (b) the Swap Exposure;

6 the Corporate Guarantor shall not pay any cash dividends to shareholders during the Waiver Period; and

7 the existing charters to COSCO Qingdao (Avoca) and COSCO Tianjin (Saldanha) shall remain in full force and effect at all times. Within thirty (30) days from cancellation either of such charters, the Waiver Period shall terminate and the application of clause 5.3 of the Corporate Guarantee and clause 8.2. I of the Facility Agreement shall revive with immediate effect except if, within such thirty (30) day period the Borrowers have presented to the Agent an alternative remedial plan acceptable in all respects to the Agent in its absolute discretion to rectify and maintain compliance with such clauses at all times.

This letter and any non contractual obligations in connection with this letter shall be governed by, and construed in accordance with, English law.

The terms of this letter shall not take effect unless and until the Agent is provided with full documentation (including without limitation, a supplemental agreement to the Facility Agreement and any security documents required thereunder) on terms and conditions acceptable to the Banks in all respect and in form acceptable to the Agent in its sole discretion.

/s/ ILLEGIBLE

Signed by:

for and on behalf of

DNB NOR BANK ASA

as Agent

We agree to the above.

Signed by:

for and on behalf of

TEAM-UP OWNING COMPANY LIMITED

Dated: [—] May 2009

Signed by:

for and on behalf of

ORPHEUS OWNING COMPANY LIMITED

Dated: [—] May 2009

Acknowledged by:

2

for and on behalf of

DRYSHIPS INC.

Dated: [—] May 2009

3