The traditional approach to handling integer problems in constraint logic programming systems is to use propagation-based finite domain solvers. These solvers are weak (they do not detect unsatisfiability of complex integer constraints in many cases), but efficiently implementable. They usually require explicit upper and lower bounds for each of the variables of the problem, and if these bounds are too large they can be very inefficient. We present an alternative approach to solving integer constraints based on a polynomial-time solver for a restricted class of integer constraints, constraints of the form ax + by d where a; b 2 f\Gamma1; 0; 1g. We use this solver as a basis for a complete integer solver, by combining it with a propagation-based solver. The resulting system improves the propagation approach on a number of different classes of problem. Key Words: constraint logic programming, linear integer constraints, constraint solving algorithms 1 Introduction Integer c..