We present an efficient method for robustly calculating time-frequency attributes of a signal, including instantaneous mean frequency, bandwidth, and kurtosis. Most current approaches involve a costly intermediate step of computing a (highly oversampled) 2-D bilinear time-frequency representation (TFR), which is then collapsed to the 1-D attribute. Using the principles of hybrid linear/bilinear time-frequency analysis, we propose computing attributes as nonlinear combinations of the (barely oversampled) linear Gabor transform of the signal. The method is both computationally efficient and accurate-it performs as well as the best bilinear techniques based on adaptive TFRs. To illustrate, we calculate an attribute of a seismic cross-section.