An algorithm is proposed for the bounded variable pure integer programming problem which treats general integer variables directly in an implicit enumeration procedure closely related to that advanced by Balas and Geoffrion for binary programming problems. Means of obtaining near optimum solutions through a slight modification of the algorithm are discussed. Techniques which use bounds on variables to improve algorithmic efficiency are developed and examined computationally. Further computational results indicate that direct treatment of general integer variables is significantly more effective than binary expansion.