A luminescence relaxation function I(t/tau(0); alpha, beta) unifying the stretched exponential with the compressed hyperbola is obtained. The scaling parameter tau(0) has dimensions of time, whereas the shape-determining parameters alpha and beta are dimensionless, both taking values between 0 and 1. For short times, the relaxation function is always exponential, with time constant tau(0). For small values of alpha, the function is close to exponential for all times. The function is also close to an exponential when beta is near unity. For large values of alpha and long times, the function is close to a stretched exponential, provided that beta > 0. The compressed hyperbola is recovered for beta = 0. (C) 2008 Elsevier B. V. All rights reserved.