JOSHUA P. STARR, the Montgomery County schools chief, has submitted a budget request of $2.2 billion for next year — and in the process needlessly picked a $10 million fight with the county, which provides most of the school system’s funding.

The amount at stake in the fight, equal to less than half of 1 percent of schools spending, is frivolous. The principle isn’t.

Ten million dollars is the gap between Mr. Starr’s request and the minimum county contribution owed to the schools according to Maryland law, which requires that per-pupil spending stay abreast of rising enrollment. Under the state formula, Montgomery is obligated to increase its contribution to the schools by $29 million next year, or 2 percent; Mr. Starr has asked for a $39 million bump.

The gap isn’t enormous in the context of a $2.2 billion budget. The problem is that when the county exceeds its state-mandated base contribution — as it did almost every year in the 2000s — it establishes a new, higher funding floor. Even in a severe economic downturn, state law makes it hard or impossible for counties to pare spending.

The effect is to protect school budgets while exposing libraries, parks, health, public safety and other services to sharp cuts. With good reason, county officials are not eager to tie their hands.

Mr. Starr made a rookie mistake in his first year as Montgomery’s superintendent. Faced with a choice between giving $65 million in pay raises to teachers and staff or devoting at least some of it to cutting class sizes or restoring classroom jobs eliminated in recent years, he gave it all to salaries — even though Montgomery teachers are already the best-paid among teachers in Washington suburban schools systems.

Now Mr. Starr wants extra funding to hire more math and middle school teachers next year, something he could have done this year.

County officials warned Mr. Starr that if he wanted to embark on new hiring or initiatives next year, he would have to find the money within the state-mandated funding formula. That should have been adequate: In addition to the $29 million increase in county funding, the schools can expect more money from the state, which provides about a quarter of the system’s revenue.

Under the current year’s schools budget, a large majority of the county’s teachers received a raise in July, and most will get another next May. Those two raises will boost an average teacher’s salary to around $80,000, up from $74,700. Mr. Starr isn’t proposing another increase for now, but he may well have to do so if state funding exceeds his modest projections, which seems likely.

Montgomery’s school system, the largest in the state, remains excellent. The question is not whether teachers deserve good salaries; they do. But it would be irresponsible for the county to once again fall into the habit of showering more funds onto the schools than it can afford.