IN RECENT YEARS SERIOUS ATTENTION HAS BEEN GIVEN TO THE POTENTIAL OF IMPRISONMENT TO REDUCE CRIME BY DETERRENCE AND BY INCAPACITATION. IN THIS MODEL, INTENDED TO GUIDE POLICY FOR CONTROLLING CRIME THROUGH IMPRISONMENT, TWO POLICY VARIABLES ARE THE CERTAINTY AND SEVERITY OF OF IMPRISONMENT (I.E., 'Q' AND 'S,' RESPECTIVELY). THE FIRST CAN BE THE PROPORTION OF CONVICTED OFFENDERS WHO ARE IMPRISONED, AND THE LATTER IS THE AVERAGE TIME SERVED BY INMATES. THE PROBABILITY OF CONVICTION GIVEN A CRIME IS AN IMPORTANT ELEMENT OF CERTAINTY. IN THE BASIC MODEL, OFFENDERS ARE ASSUMED TO COMMIT CRIMES OF A SINGLE AGGREGATE OFFENSE TYPE AT SOME HOMOGENEOUS RATE, THE AGGREGATE CRIME RATE FOR SOCIETY IS REPRESENTED AS THE PRODUCT OF THE PROPORTION OF THE POPULATION THAT IS CRIMINAL AND THE INDIVIDUAL EFFECTIVE CRIME RATE, AND THE EQUILIBRIUM IMPRISONMENT RATE PER CAPITA IS GIVEN BY THE PRODUCT OF THE CRIME RATE PER CAPITA AND THE EXPECTED MAN-YEARS OF IMPRISONMENT PER CRIME. THE PROPORTION OF THE POPULATION ENGAGING IN CRIME INCORPORATES THE DETERRENT EFFECT OF THE SANCTIONS; THE PROPORTION OF TIME A CRIMINAL IS FREE IS THE COMPLEMENT OF THE PROPORTION OF TIME HE IS IMPLEMENTED; AND THE CRIME RATE MONOTONICALLY DECREASES CONSISTENTLY WITH DECREASES IN THE CRIMINAL POPULATION AND CRIMINALS' FREE TIME PROPORTIONS. FINDING THE OPTIMUM VALUES FOR 'Q' AND 'S,' THE PROBABILITY OF IMPRISONMENT GIVEN CONVICTION, AND THE AVERAGE TIME SERVED GIVEN IMPRISONMENT IS COMPLICATED, AND THE MODEL APPROACH BEGINS BY A REPARAMETERIZATION THAT INTRODUCES A SINGLE SANCTION-LEVEL VARIABLE 'K,' THE EXPECTED SENTENCE PER CONVICTION. AN ILLUSTRATIVE EXAMPLE OF THE MODEL IN OPERATION IS PRESENTED USING 1970 DATA ON INDEX CRIMES AND THEIR SANCTIONS. THIS MODEL CONSIDERS A HOMOGENEOUS CRIMINAL POPULATION COMMITTING A SINGLE AGGREGATE CRIME TYPE. EXTENSIONS ARE NEEDED TO ACCOUNT FOR VARYING RATES AND CRIME TYPES, AND TO PROVIDE A RICHER CHARACTERIZATION OF THE COURSE OF A CRIMINAL CAREER. EMPIRICAL STUDIES ARE NEEDED TO ESTIMATE THE MODEL'S PARAMETERS. THE APPENDIX DESCRIBES THE DERIVATION OF THE OPTIMUM VALUES FOR 'Q' AND 'S.' REFERENCES AND EQUATIONS ARE PROVIDED. (DAG)