A model and method to accurately estimate the local speed of sound in tissue from pulse-echo ultrasound data is presented. The model relates the local speeds of sound along a wave propagation path to the average speed of sound over the path, and allows one to avoid bias in the sound-speed estimates that can result from overlying layers of subcutaneous fat and muscle tissue. Herein, the average speed of sound using the approach by Anderson and Trahey is measured, and then the authors solve the proposed model for the local sound-speed via gradient descent. The sound-speed estimator was tested in a series of simulation and ex vivo phantom experiments using two-layer media as a simple model of abdominal tissue. The bias of the local sound-speed estimates from the bottom layers is less than 6.2 m/s, while the bias of the matched Anderson's estimates is as high as 66 m/s. The local speed-of-sound estimates have higher standard deviation than the Anderson's estimates. When the mean local estimate is computed over a 5-by-5 mm region of interest, its standard deviation is reduced to less than 7 m/s.