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Although there is a record of purchase tied to each money order, some at city hall fear they are being used to shroud straw donors to various campaigns.

Yet council Chairman Phil Mendelson, a Democrat, showed resistance to the idea in comments Monday and Tuesday morning. He said the cap seemed too low and that money orders do, at least, leave some record of the purchase.

Ms. Cheh’s measure would comport with the law in other states. Massachusetts, for instance, decided in 1995 that political contributions made by money order could not exceed $50, the same cap it imposed on cash donations. A donation of more than $50 would have to be made by personal checks.

Mr. Gray supported her measure in his position letter to the council but noted “it is regrettable that the Council did not seize the opportunity to enact full campaign finance reforms during this Council Period.”