For low-flow data sequences that can plausibly be assumed to have a Weibull distribution, possibly with time trend superimposed, both estimation of a linear trend parameter and tests for its statistical significance are more efficient where information about the underlying Weibull distribution is incorporated into estimation and testing procedures. Both maximum likelihood and linear-regression estimates of linear trend are unbiased in sample sizes commonly found in hydrological practice (from 30 to 50 years). In samples of this relatively limited size, maximum likelihood (ML) estimates of a linear trend parameter have smaller variance than the linear regression (LR) estimate, except when the Weibull parameter k is near to one, when the distribution reduces to an exponential form. For the larger sample size used in simulation, N = 50, empirical tests based on the distribution of the ML and LR estimates showed that those based on maximum likelihood were always more powerful. However, a critical assumption in the paper is that annual low flows are independently distributed, and this may not always be justified.