Weak-lensing searches for galaxy clusters are plagued by low completeness and purity, severely limiting their usefulness for constraining cosmological parameters with the cluster mass function. A significant fraction of ‘false positives’ are due to projection of large-scale structure and as such carry information about the matter distribution. We demonstrate that by constructing a ‘peak function’, in analogy to the cluster mass function, cosmological parameters can be constrained. To this end, we carried out a large number of cosmological N-body simulations in the Ωm–σ8 plane to study the variation of this peak function. We demonstrate that the peak statistics is able to provide constraints competitive with those obtained from cosmic-shear tomography from the same data set. By taking the full cross-covariance between the peak statistics and cosmic shear into account, we show that the combination of both methods leads to tighter constraints than either method alone can provide.