We consider signals that follow a parametric distribution where the parameter values are unknown. In order to estimate such signals from noisy measurements in scalar channels, our mixture universal signal estimator (MUSE) mixes over multiple Bayesian denoisers, where the weight assigned to each parameter is its posterior density given the noisy measurements. We then apply MUSE to solve compressed sensing (CS) signal estimation problems by successively denoising a scalar Gaussian channel within an approximate message passing (AMP) framework. Our numerical results are favorable, showing that both MUSE (in scalar channels) and MUSE-AMP (in CS) approach the minimum mean square error of the Bayesian method.