Cancer progression leads to changing scattering properties of affected tissues. Single fiber reflectance (SFR) spectroscopy detects these changes at small spatial scales, making it a promising tool for early in situ detection. Despite its simplicity and versatility, SFR signal modeling is hugely complicated so that, presently, only approximate models exist. We use a classic approach from geometrical probability to derive accurate analytical expressions for diffuse reflectance in SFR that shows a strong improvement over existing models. We consider the case of limited collection efficiency and the presence of absorption. A Monte Carlo light transport study demonstrates that we adequately describe the contribution of diffuse reflectance to the SFR signal. Additional steps are required to include semi-ballistic, non-diffuse reflectance also present in the SFR measurement.