Exhibit 10.1

FIRST AMENDMENT TO EMPLOYMENT AGREEMENT

This First Amendment to Employment Agreement (“Amendment”) between Cyberonics,
Inc. (the “Company”) and Daniel Jeffrey Moore (“Executive”) shall be effective
as of April 26, 2007.

The Company and Executive entered into an Employment Agreement dated April 26,
2007 (the “Agreement”).

The Company and Executive intended to provide certain compensation and benefits
to Executive, including reimbursement of all of Executive’s reasonable expenses
related to relocation of his principal residence to the Houston area. Following
execution of the Agreement, the Company and Executive recognized that Section
9(e) embodies a mutual mistake that may frustrate the intention of the parties.

Now, therefore, for good and valuable consideration, the receipt and sufficiency
of such consideration being hereby acknowledged, and for and in consideration of
the mutual promises, covenants, and obligations contained herein, Company and
Executive agree as follows:

1. Section 9 of the Agreement is deleted in its entirety, and the following
provision is substituted therefor:

Relocation. Executive shall use his reasonable best efforts to relocate his
principal residence to the Houston area within six months following the Start
Date. Provided that Executive complies with the requirements of the Cyberonics
Executive Relocation Policy (as modified as set forth below), the Company shall
reimburse Executive’s actual, reasonable expenses, without regard to when
Executive actually relocates his principal residence, for the cost of:

  (a)   moving Executive’s household goods and possessions to the Houston area;
 

  (b)   up to three trips by Executive and Executive’s family to Houston to
locate housing in the Houston area;  

  (c)   temporary housing for the Executive in the Houston area for up to six
months from the Start Date,  

  (d)   up to twelve round trips to Boston during the period commencing on the
Start Date and continuing until the earlier of six (6) months from the Start
Date or until Executive’s family relocates to Houston, and  

  (e)   up to nine percent (9%) of the selling price of Executive’s Boston
residence to cover the sales commission and reasonable closing costs.  

2. All other terms of the Agreement shall remain unchanged.

In witness whereof, the parties have executed this Amendment to be effective as
of the 26th day of April, 2007.

Cyberonics, Inc.

By      /s/ David S. Wise     
David S. Wise, Secretary

     /s/ Daniel Jeffrey Moore     
Daniel Jeffrey Moore