direct primary

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A preliminary election in which a party's candidates for public office are nominated by direct vote of the people.

from the GNU version of the Collaborative International Dictionary of English.

• (Political Science) A primary by which direct nominations of candidates for office are made.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun US A primary in which voters directly select candidates for office by popular vote

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a primary where voters directly select the candidates who will run for office