We give new information about the geometry of closed, orientable hyperbolic 3‐manifolds with 4‐free fundamental group. As an application we show that such a manifold has volume greater than 3.44. This is in turn used to show that if M is a closed orientable hyperbolic 3‐manifold such that vol M⩽3.44, then dimℤ2 H1(M; ℤ2) ⩽ 7.