After months of agonized debate about its 110-year-old tradition of free education, Cooper Union will begin charging graduate students next year while maintaining, at least for now, its no-tuition policy for undergraduates, the college’s president said Tuesday.

Cooper Union, in the East Village, will also expand its graduate and other programs to generate more income as it searches for a way out of a deepening financial hole. Jamshed Bharucha, who became president last July, said in October that the institution had no choice but to consider making students pay, prompting a storm of protest from some students, alumni and faculty, who saw the idea as a violation of Cooper Union’s core principles.

The plan announced on Tuesday stopped far short of broad-based tuition, which might have been the simplest and surest route to financial stability. It also fell short of meeting the fiscal target that Cooper Union set last fall. In an interview, Dr. Bharucha made it clear that the college may yet have to be more aggressive about raising revenue.

“This hybrid model is exciting because it gives us a chance to do new things and not just hunker down,” Dr. Bharucha said. But, he added, “There are risks for this strategy, and there are those who worry if it will work.”