Depth of interaction (DOI) measurement is an important capability for a detector suitable for use in a small PET scanner designed for breast imaging or small animal imaging. We have investigated a different scheme to determine DOI by using a position sensitive PMT (PS-PMT) at one end of an LSO crystal array for positioning and timing, and a single channel PMT connected to the other end through bent optical fibers with the ratio of the two signals to determine DOI. The main advantage of this approach is that both the PS-PMT and PMT can provide high signal-to-noise ratio outputs (improving DOI resolution) and that all technologies are available with easy readout electronics. Therefore, the design permits a relatively simple and practical solution to measure DOI while still maintaining good detector performance. We have successfully bent optical fibers, with a light loss due to fiber bending less than 10% for bending angles from 90 to 130 degrees and for a radius of curvature from 2 to 10 mm. Preliminary measurements for a detector with 2×2×21 mm3 LSO scintillators and a Hamamatsu R5900-C8 PS-PMT reveal good DOI measurement capability with this design, the measured DOI resolution ranging from 4.2 to 6 mm. It also provides excellent crystal identification and coincidence timing performance. The attenuation and scatter effects introduced by using optical fibers were also studied.