  We present a Lagrangian approach to counting degrees of freedom in
first-order field theories. The emphasis is on the systematic attainment of a
complete set of constraints. In particular, we provide the first comprehensive
procedure to ensure the functional independence of all constraints and discuss
in detail the possible closures of the constraint algorithm. We argue degrees
of freedom can but need not correspond to physical modes. The appendix
comprises fully worked out, physically relevant examples of varying complexity.
