Biased Laplacian masks are useful for enhancing the sharpness of edges in images degraded by moderate amounts of blur and noise. Further-more, their implementation on pipelined processors is fast and convenient. However, as we show, they become limited by noise very rapidly. The use of a mask whose bias adapts to local variance measured in 3 X3 windows is explored in this paper. Results demonstrate a significant enhancement of the power of biased Laplacian masks.