We show how to account self-consistently for self-field effects upon the average transport critical current density J_c of a flat type-II superconducting strip in the mixed state when the bulk pinning is characterized by a magnetic-flux-density-dependent depinning critical current density J_p(B). We consider the possibility of both bulk and edge-pinning contributions but conclude that bulk pinning dominates over geometrical edge-barrier effects in state-of-the-art YBCO films and prototype second-generation coated conductors. For the example of the Kim model, J_{pK}(B) = J_{pK}(0)/(1+|B|/B_0), we calculate J_c(B_a) as a function of a perpendicular applied magnetic induction B_a and show how J_c(B_a) is related to J_{pK}(B). We find that J_c(B_a) is very nearly equal to J_{pK}(B_a) when B_a > B_a*, where B_a* is the value of B_a that makes the net flux density zero at the strip's edge. However, J_c(B_a) is suppressed relative to J_{pK}(B_a) for B_a < B_a*, with the largest suppression occurring when B_a*/B_0 is of order unity or larger.