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The number of vehicles that are included in a metered motorway ramp or an urban signalized link at any time is valuable information for real-time control. A recently developed Kalman-filter-based real-time estimator for the vehicle count within signalized links, using three detector cross stations, is simplified in this paper to allow for reliable estimates on the basis of one single time-occupancy measurement that is typically available in urban signalized links. The simplified vehicle-count estimator is tested and compared with the three-detector estimation scheme via microscopic simulation for a variety of scenarios and traffic conditions. Several related issues are addressed: the effect of utilizing more measurements, as well as the impact of the update period, signal cycle, vehicle length, and link length. The simulation investigations indicate less-accurate but still reasonable and robust estimation performance of the simplified estimator with low calibration effort needed, which facilitates easy applicability of the method.