We have investigated carrier sweepout in a series of strained InGaAsP multiple quantum well laser structures by time-resolved photoconductivity and CW photoluminescence. The electrons and holes exhibit very different escape times: the electrons less than 0.5 ns and the holes greater than 10 ns. With only the built-in field across the wells, the electron escape is thermally activated in both tensile samples, while it is unclear whether tunneling or thermionic emission is the dominant escape mechanism in the unstrained and compressive samples. Application of a 2 V reverse bias is sufficient to produce efficient tunneling escape of electrons in the tensile samples. A simple model of the competition between thermionic emission and radiative recombination in the tensile wells yields values for the barrier height that are in agreement with the calculated values.