Systems of hyperbolic conservation laws often present different scales linked to the magnitude of the eigenvalues of the Jacobian of the flux function. Numerical schemes used to integrate hyperbolic problems usually are explicit, because in many applications one is interested in resolving all scales. Borrowing our terminology from gas dynamics, explicit schemes resolve both convective and acoustic waves. However, when the flow is considerably slower than the sound speed, the stability condition required by an explicit scheme may become too restrictive. Moreover, the solution obtained resolves the fast scales far better than the slow ones. Thus, an implicit scheme may yield not only a more favourable computational time, but also a sharper resolution of the slow scales which may be of interest. This occurs for instance when one is more interested in the evolution of vortices rather than the propagation of the corresponding sound. In this contribution, we will focus on a class of implicit schemes designed with this purpose. The main point is to base the computation on a low order predictor, coupled with a higher order corrector. The resulting scheme provides a non oscillatory solution, degrading to first order as the scheme detects the presence of shock waves.