Many women who have mammograms get normal results that come with a caveat: They are told they have dense breast tissue, which can make their scans harder to read and could leave cancer undetected.

Sometimes those patients are advised to follow up by getting ultrasounds or magnetic resonance imaging (M.R.I.) scans, but for many, it is unclear what their next step should be.

Now, a new study provides strong evidence that supplemental M.R.I.s are more effective in finding tumors in these women than mammograms alone.

The study, of more than 40,000 women with extremely dense breasts in the Netherlands, found that those who had mammograms followed by M.R.I.s, had more tumors detected than with mammography alone. The research also found that those who had M.R.I.s were less likely to find a palpable cancerous lump in between routine screenings; by the time tumors are big enough to be felt, they tend to be more advanced.