We investigate cosmic string models for structure formation which include a non-zero cosmological constant .
We find that the background evolution of density perturbations and modifications to the scaling behaviour of the strings both act to increase the amount of power present on 100 h ^ { -1 } Mpc scales .
We estimate the size of this effect using an analytic model for the evolution of the string network and find that a bias b \sim 2 can give acceptable agreement with the current observations .
An interesting by product of these modifications is a broad peak in the cosmic microwave background ( CMB ) angular power spectrum around l = 400 - 600 .