This paper introduces and analyzes a class of nonlinear congestion control algorithms called binomial algorithms, motivated in part by the needs of streaming audio and video applications for which a drastic reduction in transmission rate upon each congestion indication (or loss) is problematic. Binomial algorithms generalize TCP-style additive-increase by increasing inversely proportional to a power k of the current window (for TCP, k=0); they generalize TCP-style multiplicative decrease by decreasing proportional to a power l of the current window (for TCP, l=1). We show that there are an infinite number of deployable TCP-compatible binomial algorithms, those which satisfy k+1=1, and that all binomial algorithms converge to fairness under a synchronized-feedback assumption provided k+l>0; k, l/spl ges/0. Our simulation results show that binomial algorithms interact well with TCP across a RED gateway. We focus on two particular algorithms, IIAD (k=1, l=0) and SQRT (k=l=0.5), showing that they are well-suited to applications that do not react well to large TCP-style window reductions.