iBASIS,INC.

Exhibit 10.1

iBASIS, INC.

June 21, 2005

To:          JMG Triton Offshore Fund, Ltd.

JMG Capital Partners, L.P.

11601 Wilshire Blvd., Suite 2180

Los Angeles,  CA  90025

Re:          8% Secured Convertible Notes due 2007

Ladies and Gentlemen:

Reference is hereby made to that certain Indenture (the “Indenture”), dated as of June 18, 2004, by and between iBasis, Inc. (the “Company”) a Delaware corporation, the Subsidiary Guarantors named therein, and The Bank of New York, a New York banking corporation, relating to the Company’s 8% Secured Convertible Notes due 2007 (the “Notes”).  Capitalized terms used herein without definition shall have the meanings given to such terms in the Indenture.

1.             Exercise of Conversion Privilege.  Pursuant to Section 15.2 of the Indenture, and in consideration for the payment described in paragraph 2 below, JMG Triton Offshore Fund, Ltd. and JMG Capital Partners, L.P. (together, “JMG”) are exercising their conversion privilege with respect to $8.0 million aggregate principal amount of Notes currently held by JMG (the “JMG Notes”), and have delivered a conversion notice in accordance with the requirements of Section 15.2 of the Indenture to effect such conversion.  In connection with such conversion, and upon the surrender and conversion of the JMG Note at the Conversion Price in accordance with the requirements of Section 15.2 of the Indenture, the Company shall issue and deliver to JMG an aggregate of 4,324,324 shares of Common Stock, $0.001 par value per share of the Company (the “Conversion Shares”), as well as a check in payment for any fractional shares.

2.             Additional Consideration. As an inducement to JMG to exercise its conversion privilege, and as a condition precedent to such conversion, the Company shall also pay JMG a cash payment of $480,000.

3.             Electronic Delivery of Shares.  To be completed only if the undersigned elects to receive delivery of the Conversion Shares electronically, rather than in certificated form, in which case the undersigned will have to provide the following information in consultation with the undersigned’s broker:

Broker Information:

The undersigned hereby acknowledges that the foregoing information is true, correct and complete, and the undersigned hereby releases, and agrees to hold harmless, the Company from any losses or liability the undersigned may suffer as a result of the electronic delivery of any shares of Conversion Shares the undersigned may be entitled to receive in connection with the Conversion pursuant to the foregoing instructions.  The undersigned further agrees and acknowledges that if the undersigned completes this section entitled “Electronic Delivery of Shares”, the undersigned will not be receiving any certificates representing the Conversion Shares, and that electronic delivery of the Conversion Shares may not be available to any individual that may be considered an affiliate of the Company under applicable law and the delivery of the Conversion Shares pursuant to this Section 3 shall satisfy in all respects the Company’s obligation, and the Company shall have not liability in connection therewith, to issue the Conversion Shares pursuant to Section 1 hereof and the Indenture.

4.             Counterparts.  This letter agreement may be signed in multiple counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.  Please contact Richard G. Tennant, at ###-###-#### should you have any questions regarding this letter agreement.

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