This paper considers the treatment of general equality and inequality path constraints in the context of the control vector parametrization approach to the optimization of dynamic systems described by mixed sets of differential and algebraic equations (DAEs) of index not exceeding 1. Equality path constraints are handled by incorporating as many of them as possible within the DAE system itself without increasing its index. This allows a subset of the control variables to be determined from the solution of the augmented DAE system. The issues involved in establishing an appropriate partitioning of the control variable vector are examined. Inequality path constraints are handled through the combined application of the discretization of these constraints at a finite number of points, and forcing an integral measure of their violation to zero. Numerical experiments demonstrating the advantages of this hybrid technique over its individual components are presented.