The first player taken in the second round, the French prospect Damien Inglis, signed with the Bucks for just over $800,000 each of the next two years, with a third year unguaranteed.

“I’ve had players, I’ve said, ‘Do you really know what you’re doing?’ ” Kentucky Coach John Calipari said. “ ‘You know you’re probably going to go in the second round. I know you’re being told you’ll go in the first round. I’m telling you, you’re going to go in the second round, maybe. What if you don’t get drafted? Are you O.K.?’ ”

While no freshmen were taken after the first round in this year’s draft, seven of them have been picked in the second round since 2010. Only two are still in the N.B.A.

Calipari has become synonymous with the one-and-done movement, or as he puts it, “succeed and proceed.” But he is among the many coaches who would prefer the rule be scrapped in the next round of collective bargaining between the N.B.A. and the players union when it expires in 2017. Calipari would prefer a two-year rule, or something similar to the rules in baseball, where prospects can turn pro out of high school but must remain in school for three years if they decide to go to college.

Adam Silver, the new N.B.A. commissioner, said in April that he was also in favor of a two-year requirement, and that such a threshold would also contribute to a better professional product.

Besides, Calipari said, many players, like his junior center Willie Cauley-Stein, already know they aren’t ready for the N.B.A.

“Willie Cauley, after the championship the next morning, we meet, and I congratulate him and tell him: ‘Hey, man, you’re in the top 15. I’m happy for you. Good luck.’ The next day he comes in and says, ‘Coach, I’m staying,’ ” Calipari said. “I go, ‘What? Tell me why.’ ‘I’m not ready to have an impact in that league and I know that. I’m going to be able to get my degree and I haven’t won a championship and I want to win a championship.’ Good reasons, so he comes back.”