Optical coherence tomography (OCT) allows structural and functional imaging of biological tissue with high resolution and high speed. Optical coherence elastography (OCE), a functional extension of OCT, has been used to perform mechanical characterization. A handheld fiber-optic OCE instrument allows high sensitivity virtual palpation of tissue with great convenience and flexibility and can be used in a wide range of clinical settings. Moreover, fiber-optic OCE instruments can be integrated into a needle device to access deep tissue. However, the major challenge in the development of handheld OCE instrument is non-constant motion within the tissue. In this study, a simple and effective method for temporally and spatially adaptive Doppler analysis is investigated. The adaptive Doppler analysis method strategically chooses the time interval (δt) between signals involved in Doppler analysis, to track the motion speed v(z,t) that varies as time (t) and depth (z) in a deformed sample volume under manual compression. The aim is to use an optimal time interval to achieve a large yet artifact free Doppler phase shift for motion tracking.