Models of contact tracing often over-simplify the effects of quarantine and isolation on disease transmission. We develop a model that allows us to investigate the importance of these factors in reducing the effective reproduction number. We show that the reduction in onward transmission during quarantine and isolation has a bigger effect than tracing coverage on the reproduction number. We also show that intuitively reasonable contact tracing performance indicators, such as the proportion of contacts quarantined before symptom onset, are often not well correlated with the reproduction number. We conclude that provision of support systems to enable people to quarantine and isolate effectively is crucial to the success of contact tracing.