On a recent morning, the baseball team, which had recently returned from a doubleheader at Azusa Pacific, a small Division II Christian college near Los Angeles, ran drills and took batting practice. The players use wooden bats in Mexico, switching to aluminum against N.C.A.A. opponents.

“We are very thankful to be able to go play and have some games,” said center fielder Marcos Almonte, “because that motivates us.”

Women’s volleyball players said they also felt challenged, in a variety of ways, when playing north of the border.

In the United States, according to several players, illegal sets are policed less strictly, griping toward the officials is less tolerated and the ball itself is lighter. “We hate it,” Yared Carmona said with a frustrated smile. “It flies away.”

Hours after their early morning departure, after the border crossing and breakfast, the day’s volleyball game turned out to be little more than an exhibition match. San Diego Christian competes in the N.A.I.A., a tier below the N.C.A.A. and its three divisions. For its players, the match was a gussied-up practice; the team did not even wear its full uniforms.

San Diego Christian may have had the edge in size. But over the course of four games, Cetys displayed superior resourcefulness and skill, with crafty sets and feinted spikes. Cetys won all four games, mounting a substantial comeback to take the final one, 25-23.

“The kind of game they play is really fast,” Maritza Alvarado, a senior, had said of American opponents. She then turned her attention to the three best-of-five competitions against Division II teams that the team would play the next day. These are the kinds of teams Cetys can expect to face if its N.C.A.A. membership comes through.

“And they’ll be better,” she said.