The status of the swift fox (Vulpes velox) became a subject of controversy when a petition was submitted in 1992 to have it listed under the provisions of the Endangered Species Act. Colorado is believed to have one of the largest remaining populations of the species due to significant amounts of short-grass prairie habitat suitable for occupancy. In 1995, we initiated a survey in eastern Colorado to determine swift fox population size and presence or absence on 724.8×6.4 km² grids trapped with 20 live traps. We drew trapping grids from a stratified random sample of grids plotted on 1:100,000 scale Gap vegetation maps of eastern Colorado. Of the grids sampled, 54% were from areas with 75% short-grass habitat. We captured 241 swift foxes (117 male, 121 female, and 3 undetermined) on 51 (71%) of the grids. We estimated a mean capture probability per night of an individual fox, weighted by number of grids and number of trapping occasions for each grid, as 0.234 (SE = 0.022). Highest capture and detection probabilities occurred during the September to March period. We estimated the average number of foxes per grid as 6.96 (SE = 0.794), likely a maximum estimate because of foxes being attracted to the trapping grids. Percentage of short-grass prairie habitat on each grid was an important predictor of both occupancy rate and detection probabilities. We estimated occupancy rate of the 72 grids trapped as 0.821 (SE = 0.0659), using the mean (66.9%) of the short-grass prairie habitat for the 72 grids as a covariate, suggesting that 59.1 (SE = 4.74) of the 72 grids trapped contained foxes. Alternatively, using the percentage of short grass prairie for each grid to estimate a grid-specific occupancy probability, we estimated 56.9 (SE = 4.13) of the 72 grids contained foxes. We estimated nightly detection probabilities of >0.60 for grids trapped in March. We used simulation to compute the power to detect simulated changes in occupancy rates assuming a detection probability of 0.6 and an occupancy rate of 0.8. With only 2 trapping occasions, even with 100 trapping grids, the power was only 80% to detect a change in occupancy from 0.8 to 0.5. With 50 trapping grids and 3 trapping occasions, the power was nearly 80% to detect a 0.3 reduction in occupancy rate and >80% for 4 trapping occasions.