A particle with fixed speed v that simultaneously wants to behave evasively and drift from one point to another in two dimensions has a conflict: If it drifts the maximum distance vt in a fixed time t, then it is forced to travel in an absolutely unevasive straight line. On the other hand, drift will not be maximal if the particle's motion is some sort of an evasive random walk. The purpose of this note is to report on an exploration of quantitative tradeoffs between these objectives. (Author)