This paper explores how the capacity of colonoscopy services should be allocated for screening and diagnosis of colorectal cancer to improve health outcomes. Both of these services are important since screening prevents cancer by removing polyps, while diagnosis is required to start treatment for cancer. This paper first presents a basic compartmental model to illustrate the trade-off between these two analytically. Further, a more realistic population dynamics model with resource constraints is introduced for colorectal cancer screening and analyzed numerically. The best resource allocation decisions are investigated with the objectives of minimizing mortality or incidence rates. We provide a sensitivity analysis with respect to policy and disease-related parameters. We conclude that to minimize mortality, the capacity should be rationed to ensure that the wait for diagnosis is at reasonable levels. When the relevant performance measure is the incidence rate, screening is allocated more capacity compared to the case with mortality rate measure. We also show that benefits from increasing compliance to screening programs can only be realized if there is sufficient service capacity.