In this paper, we introduce an adaptive L-p-norm metric for robust coherent diversity combining in non-Gaussian noise and interference. We derive a general closed-form expression for the asymptotic bit error rate (BER) for L-p-norm combining in independent non-identically distributed Ricean fading and non-Gaussian noise and interference with finite moments. Based on this asymptotic BER expression, the metric parameters can be adapted to the underlying type of noise and interference using a finite difference stochastic approximation (FDSA) algorithm. Simulation results confirm the validity of the derived asymptotic BER expression and the excellent performance of the proposed adaptive L-p-norm metric.