Let Wn,k be the Stiefel manifold U(n)/U(n - k). For odd primes p and for k ⩽ (p - 1)(p - 2), we give a homotopy decomposition of the based loop space ΩWn,k as a product of p - 1 factors, each of which is the based loops on a finite H-space. Similar decompositions are obtained for Sp(n)/Sp(n - k) and O(n)/O(n - k) and upper bounds on the homotopy exponents are obtained.