Abstract: Random coincidences degrade the image in Positron Emission Tomography, PET. To compensate for their degradation effects, the rate of random coincidences should be estimated. Under certain circumstances, current estimation methods fail to provide accurate results. We propose a novel method, “Singles-Prompts” (SP), that includes the information conveyed by prompt coincidences and models the pile-up. The SP method has the same structure than the well-known “Singles Rate” (SR) approach. Hence, SP can straightforwardly replace SR. In this work, the SP method has been extensively assessed and compared to two conventional methods, SR and the delayed window (DW) method, in a preclinical PET scenario using Monte-Carlo simulations. SP offers accurate estimates for the randoms rates, while SR and DW tend to overestimate the rates (similar to 10%, and 5%, respectively). With pile-up, the SP method is more robust than SR (but less than DW). At the image level, the contrast is overestimated in SR-corrected images, + 16%, while SP produces the correct value. Spill-over is slightly reduced using SP instead of SR. The DW images values are similar to those of SP except for low-statistic scenarios, where DW behaves as if randoms were not compensated for. In particular, the contrast is reduced, -16%. In general, the better estimations of SP translate into better image quality.