In this paper we develop a numerical formulation for simulating gas microflows in the slip-flow regime for which the Knudsen number is less than 0.3. We consider both long flat channels as well as grooved channels in order to model geometric-complexity, separation and surface roughness in micro-flows. We first modify a high-order slip boundary condition developed in our previous work so that it can be easily implemented to provide enhanced numerical stability. We also extend a previous formulation for incompressible flows to include compressibility effects which are primarily responsible for the nonlinear pressure distribution in microchannel flows. The focus of the paper is on the competing effects of compressibility and rarefaction in internal flows in long channels. Several simulation results are presented and comparisons are provided with experimental data of different research groups. In addition, the effects of thermal creep caused by tangential temperature gradients are analyzed.