Appropriately transformed, the classic analytical description of the counterflow regenerator lends itself to straightforward algebraic solution. Flushing ratios of any magnitude are accommodated, and all regimes of solution are described from initial blow through to cyclic equilibrium. The uniform particle velocity of the original treatment may be substituted by simple harmonic motion without complication, affording insight into conditions in the Stirling engine. Temperature recovery ratio is shown to be an inadequate guide to overall thermal performance. A more revealing index is derived by taking pumping loss into consideration. Design charts are presented.