This paper considers a software reliability model which allows for two types of imperfect debuggings at each failure of the software system. For one type of imperfect debugging, a fault that causes the failure is imperfectly debugged without altering the fault contents of the software system. For the other type of imperfect debugging, the fault is not only imperfectly debugged, but also a new fault is generated and introduced into the system. The probability of perfect debugging is assumed to be an increasing function of the number of debuggings performed prior to the current failure of the system. Based on the software reliability model presented, we consider three profit models to determine the optimal software release times which maximize the expected software profit. These models consider: (1) constant life cycle, (2) random life cycle, (3) random life cycle and penalty cost which is imposed when the software is delivered late. The optimal release times are shown to be finite and unique. Numerical examples are provided for illustrative purposes.