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Let G = (V,E) be a simple graph and s and t be two distinct vertices of G. A path in G is called l-bounded for some l ∈ N if it does not contain more than l edges. We prove that computing the maximum number of vertex-disjoint l-bounded s, t-paths is APX-complete for any l ≥ 5. This implies that the problem of finding k vertex-disjoint l-bounded s, t-paths with minimal total weight for a given number k ∈ N, 1 ≤ k ≤ |V| - 1, and nonnegative weights on the edges of G is NPO-complete for any length bound l ≥ 5. furthermore, we show that these results are tight in the sense that for l ≤ 4 both problems are polynomially solvable, assuming that the weights satisfy a generalized triangle inequality in the weighted problem. Similar results are obtained for the analogous problems with path lengths equal to l instead of at most l and with edge-disjointness instead of vertex-disjointness.