Intermolecular multiple-quantum coherences (iMQCs) have been reported to offer a sensitivity to sample structure at a specific user-defined length scale down to the order of 10 microm. When assessing this novel contrast mechanism in controlled phantom experiments, we have observed three different mechanisms whereby residual single-quantum coherences (SQCs) arising from intense high spatial frequencies, stimulated echoes and strong spatially encoding gradients can produce significant changes in signal contrast at particular length scales. These changes which only appear when components arising from SQCs and iMQCs are both present in the detected signal, are similar to changes previously attributed to iMQCs alone. We demonstrate each mechanism by which these residual SQCs arise and describe methods for their suppression.