Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the absorbed optical energy density within tissue. If the object possesses spatially variant acoustic properties that are unaccounted for by the reconstruction algorithm, the estimated image can contain distortions. While reconstruction algorithms have recently been developed for compensating for this effect, they generally require the objects acoustic properties to be known a priori. To circumvent the need for detailed information regarding an objects acoustic properties, we have previously proposed a half-time reconstruction method for PACT. A half-time reconstruction method estimates the PACT image from a data set that has been temporally truncated to exclude the data components that have been strongly aberrated. In this approach, the degree of temporal truncation is the same for all measurements. However, this strategy can be improved upon it when the approximate sizes and locations of strongly heterogeneous structures such as gas voids or bones are known. In this work, we investigate PACT reconstruction algorithms that are based on a variable temporal data truncation (VTDT) approach that represents a generalization of the half-time reconstruction approach. In the VTDT approach, the degree of temporal truncation for each measurement is determined by the distance between the corresponding transducer location and the nearest known bone or gas void location. Reconstructed images from a numerical phantom is employed to demonstrate the feasibility and effectiveness of the approach.