Phase and intensity from correlation and spectrum only (PICASO) is a simple and accurate method for fully characterizing femtosecond pulses. We extend this technique to make use of third-order intensity correlations. Unbalancing the interferometer makes the retrieval algorithm sensitive to the direction of time and improves the retrieval of certain pulse shapes. We investigate the sensitivity of the retrieval to direction of time as a function of the degree of imbalance in the correlator.