(CNN) A CNN/Des Moines Register/Mediacom poll in Iowa finds that a majority of likely Democratic caucusgoers would prefer a health care option that isn't "Medicare for All."

About a third (36%) want Medicare for All while another third (34%) want to create a public option for buy in and 20% would prefer to restore lost provisions from the Affordable Care Act and work incrementally from there.

Together, a majority (54%) would prefer an option that isn't Medicare for All, while only 36% prefer the more liberal alternative.

Likely attendees of the Democratic caucus who support Vermont Sen. Bernie Sanders or Massachusetts Sen. Elizabeth Warren as their first choice are more likely to support Medicare for All than supporters of other candidates (77% and 68% want Medicare respectively).

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