Cancer screening poses a quandary for women with dense breast tissue. They’re at elevated risk for breast cancer, but mammograms often miss tumors buried in dense breasts — and insurers often resist paying for additional scans that may help find the masses.

Now a large study comparing various types of scans has found that mammography enhanced with iodine-based dye can detect three times as many invasive cancers in dense breast tissue as ultrasound.

And so-called contrast-enhanced mammography can find tumors that are much smaller than those found by regular mammography. M.R.I.s are better at detecting more tumors than standard mammograms, the study found, but are considerably more expensive.

The scans were given to women with dense breast tissue who had already undergone mammograms that hadn’t turned up any abnormalities.

“Contrast-enhanced mammography needs to become standard of care for women with dense breasts,” if they are at high risk of developing breast cancer, said Dr. Fiona J. Gilbert, a professor of radiology at the University of Cambridge’s School of Clinical Medicine. She is lead author of the study, which was published Wednesday in The Lancet.

Tumors typically show up as white spots on mammograms, but dense breast tissue also appears white, obscuring the tumors.