Improved speech recognition performance can often be obtained by combining multiple systems together. Joint decoding, where scores from multiple systems are combined during decoding rather than combining hypotheses, is one efficient approach for system combination. In standard joint decoding the frame log-likelihoods from each system are used as the scores. These scores are then weighted and summed to yield the final score for a frame. The system combination weights for this process are usually empirically set. In this paper, a recently proposed scheme for learning these system weights is investigated for a standard noise-robust speech recognition task, AURORA 4. High performance tandem and hybrid systems for this task are described. By applying state-of-the-art training approaches and configurations for the bottleneck features of the tandem system, the difference in performance between the tandem and hybrid systems is significantly smaller than usually observed on this task. A log-linear model is then used to estimate system weights between these systems. Training the system weights yields additional gains over empirically set system weights when used for decoding. Furthermore, when used in a lattice rescoring fashion, further gains can be obtained.