The study of cognition, perception, and behavior often requires the estimation of thresholds as a function of continuous independent variables (e.g., contrast threshold as a function of spatial frequency, subjective value as a function of reward delay, tracking speed as a function of the number of objects tracked). Unidimensional adaptive testing methods make estimation of single threshold values faster and more efficient, but substantial efficiency can be further gained by taking into account the relationship between thresholds at different values of an independent variable. Here we present a generic method — functional adaptive sequential testing (FAST) — for estimating thresholds as a function of another variable. This method allows efficient estimation of parameters relating an independent variable (e.g., stimulus spatial frequency; or reward delay) to the measured threshold along a stimulus strength dimension (e.g., contrast; or present monetary value). We formally describe the FAST algorithm and introduce a Matlab toolbox implementation thereof; we then evaluate several possible sampling and estimation algorithms for such two-dimensional functions. Our results demonstrate that efficiency can be substantially increased by considering the functional relationship between thresholds at different values of the independent variable of interest.