Multiple shooting is a standard technique for the numerical solution of boundary value problems. We discuss the application of multiple shooting techniques to a certain class of nonlinear singular boundary value problems. Particular attention is paid to the methodology for the integration of the underlying initial value problems. To this end we use the implicit Euler scheme, serving as a basic method for the acceleration technique known as Iterated Defect Correction. This yields a stable inital value integrator realizing a high order approximation for the singular case (a nontrivial result). Simple shooting based on this integration method performs successfully, and the extension to multiple shooting is straightforward. A number of experimental results illustrating this approach are presented.