The H-free process starts with the empty graph on n vertices and adds edges chosen uniformly at random, one at a time, subject to the condition that no copy of H is created, where H is some fixed graph. When H is strictly 2-balanced, we show that for some c, d > 0, with high probability as n → ∞, the final graph of the H-free process contains no subgraphs F on v F ≤ n d vertices with maximum density max J⊆F {e J /v J } ≥ c. This extends and generalizes results of Gerke and Makai for the C 3 -free process.