While the benefit of prostate-specific antigen (PSA) based screening is uncertain, a significant proportion of screen-detected cases is overdiagnosed. In order to make screening worthwhile, it is necessary to find policies that minimize overdiagnosis, without significantly increasing prostate cancer mortality (PCM). Using a microsimulation model (MISCAN) we project the outcomes of 83 screening policies in the US population, with different start and stop ages, screening frequencies, strategies where the PSA value changes the screening frequency, and strategies in which the PSA threshold (PSAt) increases with age. In the basecase strategy, yearly screening 50-74 with a PSAt of 3, the lifetime risk of PCM and overdiagnosis equals, respectively, 2.4 and 3.8%. The policies that reduce overdiagnosis the most (for maximum PCM increases relative to basecase of 1%, 3%, and 5%, respectively) are with a PSAt of 3, (1) yearly screening 50-74 where, if PSA <1 at age 65 or older, frequency becomes 4 years, with 3.6% (5.9% reduction), (2) 2-year screening 50-72, with 2.9% (24.3% reduction), and (3) yearly screening 50-70 (PSAt of 4 after age 66), with 2.2% (43.4% reduction). Stopping screening at age 70 is a reasonable way to reduce the harms and keep the benefit. Decreasing the stopping age has a larger effect on overdiagnosis reduction than reducing the screen frequency. Screening policies where the frequency of screening depends on PSA result or in which the PSAt changes with age did not substantially improve the balance of harms and benefits relative to simple yearly screening.