We propose a small-animal PET scanner design combining two sets of monolithic crystals with two different thicknesses. The detectors with thinner crystals serve for high resolution imaging while the thicker crystals retain the detection efficiency. Two small-animal PET models based on 10 and 12 detector blocks made of monolithic LYSO crystals were implemented in the GEANT4 Monte Carlo toolkit. In each of these models, half of the detector blocks consisted of a crystal thickness of 10 mm whereas the second half had a crystal thickness of 2 mm. The scintillator crystals were coupled to SiPM arrays. For the first model, the detector blocks were arranged in a full-ring polygonal geometry in such a way that detector blocks with the same thickness were sitting opposite to each other. For the second model, detector blocks with different crystal thicknesses were facing each other. The performance of the proposed PET models was assessed using standard parameters, including spatial resolution, sensitivity and noise equivalent count rate. Comparison was made with conventional PET models with crystal thicknesses of 2 mm, 6 mm and 10 mm. PET models with a crystal thickness of 2 mm led to the highest spatial resolution (up to 0.6 mm FWHM) at the cost of poor absolute sensitivity (2.5%). On the other hand, PET models with a crystal thickness of 10 mm led to good detection efficiency (4.4%), yet with substantial degradation of spatial resolution (1.2 mm FWHM). The proposed PET models with thick and thin crystals exhibited an optimal trade-off between spatial resolution and sensitivity outperforming the PET model with fixed 6 mm crystal by achieving a spatial resolution of 0.7 mm and absolute sensitivity of 3.7%. The novel proposed PET design concept achieved an optimal trade-off between the sensitivity and spatial resolution by combining two sets of monolithic crystals.