We extend Bouwer and Rice (1976) slug test theory to incorporate background head trends that may be important in incompressible material of low permeability k. The extension, which features a convolution integral of the background head, is closed form for linear trends. A sensitivity study suggests that a rising background head can diminish the head changes associated with a slug-out test and underestimate k if it is ignored, as does falling background trend with a slug-in test. A falling background head can reinforce slug-in test head change and, if ignored, can overestimate k, as does a rising background head with a slug-out test. The simple extension is verified by field tests in glacial till and stratified drift deposits in eastern Massachusetts.