THE STUDY EXPLORES THE STATISTICAL PROPERTIES OF THE INEQUALITY CONSTRAINED LEAST SQUARE ESTIMATOR (ICLS). TO ILLUSTRATE ITS USE, THE STUDY INTRODUCES SEVERAL MODELS OF COMMUNITY EXPENDITURE ON POLICE SERVICES. THE MODELS CONCERN THE FACTORS WHICH DETERMINE THE SUPPLY OF POLICE SERVICE. THE DECISION ON THE LEVEL OF POLICING IS BASED UPON DEMAND VARIABLES (WEALTH OF RESIDENTS, LEVEL OF PROPERTY, AND VIOLENT CRIME, AND ON MOBILITY OF RESIDENTS) AND SUPPLY VARIABLE (EFFECTIVENESS OF POLICING, COMMERCIAL ESTABLISHMENTS WHICH SHOULD BE PROTECTED, AND RESOURCE AVAILABILITY). THE GENERAL MODEL AND THE ASSUMPTION USED ARE DESCRIBED. CONSTRAINT GENERALIZATIONS ARE THEN CONSIDERED IN DETAIL AND THE SMALL SAMPLE PROPERTIES OF THE ICLS ESTIMATORS DISCUSSED. THE USE OF THE ICLS ESTIMATOR IS THEN ILLUSTRATED BY AN EMPIRICAL CASE STUDY ON POLICE EXPENDITURES. FINALLY THE INTERPRETATIONS AND CONCLUSIONS OF THE ICLS ESTIMATORS ARE ANALYZED IN THE LIGHT OF THEIR USEFULNESS IN APPLIED MODELING. RESULTS DEMONSTRATE THE USEFULNESS OF THE CONSIDERATION OF CONSTRAINTS IN MODELING CRIMINAL BEHAVIOR AND SUGGEST OTHER AREAS OF ANALYSIS WHERE THESE TECHNIQUES MAY BE SIMILARLY USEFUL SUCH AS ANALYSIS OF CONSUMPTION FUNCTION OR PRODUCTION FUNCTION DATA. THE STUDY ALSO ILLUSTRATED THAT MULTICOLLINEARITY COULD BE REDUCED BY USING SEARLE'S TECHNIQUE. TABULAR DATA AND REFERENCES ARE INCLUDED. (MJW)