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Cross-correlation based time delay estimates (TDE) can be used for direction-of-arrival (DOA) estimation with an acoustic array in not-too-reverberant environments. In order to benefit from the computational efficiency of TDE-based DOA estimation, and concentrating on applications that use a compact microphone array and low sampling frequency, we use a combination of approaches to make TDE-based DOA estimation more robust under reverberant conditions. Cross-correlation interpolation based on the Goertzel algorithm is used for generalized cross-correlation TDE as well as in the steered-response-power algorithm used for comparison. The generalized cross-correlation TDE algorithm precedes a robust TDE-to-DOA process. The latter includes DOA and cross-correlation dependent weighting of the various TDE and removal of an outlier TDE. When the use of TDE from consecutive frames is possible, further performance improvement results from unit-norm DOA adaptation. Performance is evaluated for simulated and recorded data.