But he has become so fanatical that he unlaces his shoes in his elevator before he enters his Chelsea apartment, and has buyers take shoes off at most of his open houses. “Just look at a sidewalk in New York and you know where that seller is coming from,” Mr. Steinberg said.

There are dangers, he acknowledges, with some buyers “close to breaking their necks” when they try to take their shoes off standing in the doorway.

At his open house last week, Mr. Sukenik told potential buyers that children lived in the apartment and asked them to take off their shoes in the hallway or cover their shoes with surgical booties, the kind that doctors wear in the operating room, which he provided.

Mr. Sukenik said that in the past, some buyers, especially hedge fund executives who view it “humbling” to bare their feet, have angrily stormed out. But Mr. Sukenik, who wore the booties himself during the open house, said that none of the 28 visitors complained and that they seemed to appreciate the apartment’s immaculate condition.

One of them, Hayley Cohen, 27, said that it was the first time she had been asked to take off her shoes at an open house. “It was a little weird,” she said, describing how she arrived to a lineup of shoes in the hallway.