High-gradient, pressurized RF cavities are investigated as a means to improve the capture efficiency, to effect phase rotation to reduce momentum spread, and to reduce the angular divergence of a muon beam. Starting close to the pion production target to take advantage of the short incident proton bunch, a series of pressurized RF cavities imbedded in a strong solenoidal field is used to capture, cool, and bunch the muon beam. We discuss the anticipated improvements from this approach to the first stage of a muon cooling channel as well as the requirements of the RF cavities needed to provide high gradients while operating in intense magnetic and radiation fields.