This paper presents a computational algorithm to predict highly-transient flame behavior in counterflow situations. The first objective of the paper is to extend the transient counterflow problem to incorporate some gasdynamic compressibility effects, yet retain the desirable similarity structure. By relaxing assumptions in earlier formulations, the computational algorithms can deliver high accuracy even in periods of extremely rapid transients, like combustion ignition. The algorithms are demonstrated on two combustion-ignition problems for methane-air, counterflow nonpremixed flames. The first concerns the ignition transient in a steady strain field. The second concerns the effects of a high-frequency oscillatory strain field on the ignition process. The results reveal that, when the mean strain rate is near the steady ignition limit. the ignition process is highly sensitive to the details of the strain-rate fluctuations.