In this paper we present a new adaptive short-time Fourier analysis-synthesis scheme and demonstrate its efficacy in speech enhancement. While a number of adaptive analyses have previously been proposed to overcome the limitations of fixed-resolution schemes, we propose here a modified overlap-add procedure that enables efficient resynthesis. Our adaptation scheme extends earlier work using local measures of time-frequency concentration, and is applicable to power spectral density estimation for the case of noisy speech. We provide evidence of increased gains in signal-to-noise ratios for synthetic signals as well as empirical evidence of reduced musical noise based on expert listening tests for voiced and phonetically balanced utterances observed in noise, relative to a standard baseline speech enhancement system whose time-frequency resolution is fixed.