We obtain cosmological solutions of the low energy heterotic string assuming Calabi-Yau compactification with non-minimal curvature terms (R(ABCD)2 - 4R(AB)2 + R2). In particular we address the problem of which initial conditions to choose, since on emergence from the quantum gravity era, they are as yet undeterminable. We find that specific constraints are necessary on the initial-value phase space to be compatible with acceptable late-time behaviour.