In this paper, we present a novel approach to scintimammography that is based on the Compton camera principle. We analyse the performance of our scheme using Monte Carlo simulations. In particular, we evaluate the detection efficiency, spatial resolution and lesion visibility of the system at several gamma photon energies. The simulation results show that the proposed technique achieves an absolute detection efficiency of 0.03 and a full width at half maximum resolution of 3.8 mm at 141 keV photon energy for point sources 2.5 cm deep in a 5 cm thick breast phantom using 5 mm thick silicon detectors. Furthermore, our approach shows good performance in lesion detection, especially at high gamma photon energies, where mechanically collimated systems perform poorly due to severe septal penetration. With total collected counts of 1.35 million, equivalent to a 30 s acquisition time for an activity concentration level of 3.7 kBq ml-1 (100 nCi cm-3) in normal breast tissue, and a tumour-to-background ratio of 8:1, our system can clearly reveal an 8 mm diameter tumour that is located 2.5 cm deep in a 500 ml breast phantom. We also present a simulation-based quantitative performance comparison between the proposed scintimammographic system and the compact collimated scintimammographic system in the task of lesion detection under a clinical imaging situation using a non-prewhitening matched filter observer model. Our comparison demonstrates that for the same imaging time, the two systems have a comparable performance in detecting an 8 mm tumour at 141 keV, with the proposed system performing marginally better. However, the proposed scintimammographic system clearly outperforms the compact collimated counterpart in the detection of a 5 mm tumour. We also investigate the contribution of scatter and direct radiation from adjacent organs. We find that the background contribution of liver to the right breast is 30% at 141 keV, which can be reduced to 4.8% with shielding.