This study analyzes the manner in which certain favorable shifts in labor demand affect job search. Although all shifts increase reservation wages, they do not necessarily decrease expected unemployment spell durations and increase expected post-unemployment wages, so that upward-sloping short-run Phillips curves may occur. A result due to Chamberlain is used to demonstrate that if the wage offer distribution is restricted to be logconcave, two of the shifts guarantee downward-sloping Phillips curves. For one of these two shifts, previous research by Flinn and Heckman used logconcavity in a different manner to achieve properly shaped Phillips curves.