We discuss the problem of detecting local signals that occur at the same location in multiple one dimensional noisy sequences, with particular attention to relatively weak signals that may occur in only a fraction of the sequences. We propose statistics that combine data across sequences and show that they have better power properties and provide a more easily interpreted summary of the data than do procedures based on a separate analysis for each sequence. In particular, we examine the case where the signal is a temporary shift in the mean of independent Gaussian observations. The formulation of the model is motivated by the problem of detecting recurrent DNA copy number variants in multiple samples, and our results are illustrated by applications to data involving DNA copy number changes.