Let α: [0, 1] → [0, 1] be a measurable function. It was proved by P. Marchal [2] that the function (Formula Presented) is a special Bernstein function. Marchal used this to construct, on a single probability R^(a) such that (Formula Presented) space, a is the subordinator with Laplace exponent φ^(ɑ)) and R^(ɑ) ⊂ R(β) whenever ɑ ≤ β. We give two simple proofs showing that φ^(ɑ) is a complete Bernstein function and extend Marchal’s construction to all complete Bernstein functions.