Laser pump-X-ray probe experiments require control over the X-ray pulse pattern and timing. Here, the first use of pseudo-single-bunch mode at the Advanced Light Source in picosecond time-resolved X-ray absorption experiments on solutions and solids is reported. In this mode the X-ray repetition rate is fully adjustable from single shot to 500 kHz, allowing it to be matched to typical laser excitation pulse rates. Suppressing undesired X-ray pulses considerably reduces detector noise and improves signal to noise in time-resolved experiments. In addition, dose-induced sample damage is considerably reduced, easing experimental setup and allowing the investigation of less robust samples. Single-shot X-ray exposures of a streak camera detector using a conventional non-gated charge-coupled device (CCD) camera are also demonstrated.