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Arrays of silicon photo-multipliers (SiPMs) are good candidates for the readout of detectors in PET/MR inserts due to their high packing density, efficiency, low bias voltage and insensitivity to magnetic fields. We tested two dual-layer blocks of pixellated lutetium oxy-orthosilicate (LYSO) coupled to SensL 4 × 4 SiPM arrays in terms of their ability to resolve all elements using resolvability index (RI) defined by the FWHM of the crystal response function divided by the separation. Our crystal blocks had 49 1.67 × 1.67 × 6.0 mm3 crystals on the bottom layer and 36 1.67 × 1.67 × 4.0 mm3 crystals in the top layer (offset by 1/2 of the crystal pitch). All 85 crystals were well resolved: compared with for a conventional pre-clinical PET scanner's block with 40% lower crystal density. A pair of crystal blocks mounted on translation stages scanned a 0.25 mm 22Na source in 60 0.25 mm steps with the detectors angulated as if there were 16 blocks in a ring. The FWHM of the coincidence response function near the centre of the field of view was 1.31 mm and FWTM was 2.7 mm with the detectors separated by 200 mm.