We present new cosmic microwave background (CMB) anisotropy results from the combined analysis of the three flights of the first Medium Scale Anisotropy Measurement (MSAM1). This balloon-borne bolometric instrument measured about 10 deg2 of sky at half-degree resolution in four frequency bands from 5.2 to 20 cm-1 with a high signal-to-noise ratio. Here we present an overview of our analysis methods, compare the results from the three flights, derive new constraints on the CMB power spectrum from the combined data, and reduce the data to total power Wiener-filtered maps of the CMB. A key feature of this new analysis is a determination of the amplitude of CMB fluctuations at l ~ 400. The analysis technique is described in a companion paper (L. Knox).