The purpose of this study is to investigate the feasibility and impact of incorporating deliverable monitor unit (MU) constraints into spot intensity optimization (SIO) in intensity-modulated proton therapy (IMPT) treatment planning. The current treatment planning system (TPS) for IMPT disregards deliverable MU constraints in the SIO routine. It performs a post-processing procedure on an optimized plan to enforce deliverable MU values that are required by the spot scanning proton delivery system. This procedure can create a significant dose distribution deviation between the optimized and post-processed deliverable plans, especially when small spot spacings are used. In this study, we introduce a two-stage linear programming approach to optimize spot intensities and constrain deliverable MU values simultaneously, i.e., a deliverable SIO (DSIO) model. Thus, the post-processing procedure is eliminated and the associated optimized plan deterioration can be avoided. Four prostate cancer cases at our institution were selected for study and two parallel opposed beam angles were planned for all cases. A quadratic programming based model without MU constraints, i.e., a conventional SIO (CSIO) model, was also implemented to emulate commercial TPS. Plans optimized by both the DSIO and CSIO models were evaluated for five different settings of spot spacing from 3 to 7 mm. For all spot spacings, the DSIO-optimized plans yielded better uniformity for the target dose coverage and critical structure sparing than did the CSIO-optimized plans. With reduced spot spacings, more significant improvements in target dose uniformity and critical structure sparing were observed in the DSIO than in the CSIO-optimized plans. Additionally, better sparing of the rectum and bladder was achieved when reduced spacings were used for the DSIO-optimized plans. The proposed DSIO approach ensures the deliverability of optimized IMPT plans that take into account MU constraints. This eliminates the post-processing procedure required by the TPS as well as the resultant deteriorating effect on ultimate dose distributions. This approach therefore allows IMPT plans to adopt all possible spot spacings optimally. Moreover, dosimetric benefits can be achieved using smaller spot spacings.