A semi-regular sequence in S=k[x1, …, xn] is a sequence of polynomials f1, …, fr of degrees d1, …, dr which satisfy a certain generic condition. Suppose that I⊂S is generated by such a semi-regular sequence and let ρ be the Castelnuovo–Mumford regularity of S/I. We show that a minimal free resolution of S/I is isomorphic to the Koszul complex on f1, …, fr in degrees ≤ρ−2. If a common numerical condition is satisfied, then this isomorphism also holds in degree ρ−1. Therefore, the Betti diagram of S/I and the Betti diagram of the Koszul complex always agree in rows ≤ρ−2; we can sometimes determine that they also agree in row ρ−1. We also give a partial converse, that if the Betti diagram of S/I agrees with the diagram of the Koszul complex except in possibly the last two rows, then I can be generated by a (not necessarily minimal) semi-regular sequence.