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As he barnstormed in upstate New York on Saturday, Donald J. Trump came up with a new moniker for Hillary Clinton and strongly suggested that some delegates were getting a “payoff” to back certain candidates.

“Crooked Hillary!” Mr. Trump, at a rally in Watertown, N.Y., intoned about Mrs. Clinton, whom he previously called “incompetent Hillary.” But that adjective had four syllables, and Mr. Trump tends to pick names for his opponents that are shorter and likelier to stick with voters.

And he suggested that Senator Ted Cruz, his main rival for the nomination, favors the Trans-Pacific Partnership trade agreement because “somebody is probably taking care of him,” insinuating that Mr. Cruz is making decisions based on donor interests.

Mr. Trump also said in Watertown and in an earlier interview with Fox News that he thought delegates to the national convention not bound to a candidate back whichever campaign lavished goodies on them. Mr. Cruz has outmaneuvered Mr. Trump in getting his supporters named as delegates, but in Mr. Trump’s telling, it had little to do with organizational effort.

Mr. Trump said he did not want to “waste” money “to wine and dine and to essentially pay off all these people, because a lot of it’s a payoff, you understand that.”

The argument is an extension of his fight with the Republican National Committee, which he has accused of rigging rules to make it harder for him to get the nomination. He has expanded his team to bring on the seasoned Republican hands Paul Manafort and Rick Wiley to help him navigate the delegate process.

Mr. Manafort has expansive purview in the Trump campaign, but the most challenging task he or any adviser faces is controlling Mr. Trump’s message, which is frequently shoot-from-the-lip and ad-libbed. But in Watertown and in Syracuse earlier in the day, Mr. Trump kept his speech tighter, reading off a series of labor statistics.

“A couple more horrible factors here,” Mr. Trump said in Watertown, ticking off numbers showing a weakened manufacturing base in an economically depressed area.

But he called the area – which is not a frequent stop for presidential candidates – a beautiful one with prime real estate.

“Now I know why they call it Watertown – because I flew over it, and there’s a lot of water,” Mr. Trump said. “I always say, you never, in real estate, never lose money with water. Rivers, lakes and oceans. So we should be making lots of money up here folks, because you’ve got plenty of lakes and plenty of water.”