A comparison is made between computed phase sensitivities of the output intensities of twelve different types of optical fibre single-loop resonators using a non-planar or planar (collinear) 3 × 3 fibre coupler. The dependence of the phase sensitivities on major parameters of the fibre and the 3 × 3 fibre coupler is investigated. It is found that four types of fibre resonators (the PFPOFR1, PFPOFL5, TFPOFR and PFPOFR3) have high phase sensitivities (they are the highest phase sensitivities among many passive fibre ring and loop resonators with one to two 2 × 2 or 3 × 3 fibre couplers), while those of the rest are relatively small. These four types of fibre resonators may therefore be used as optical sensors.