The infamously uptight River House might be making an effort, faced with faltering sales, to modernize, as the board recently lifted its ban on residents mentioning the building's name or address in press and listings. (Still frowned upon: speaking the name out loud, looking directly at the facade, mirth.) The apartments themselves, however, remain as they've ever been—beautiful, stuffy monuments to old money New York, and prospective buyers, if there are any, have quite the inventory to choose from. Fourteen of the building's units are currently on the market, the newest of which is a 4BR on the third floor just listed for $7.35 million. To give you an idea of how things are going at River House, a slightly larger apartment on the same floor was listed for $24.5 million in 2009 and made it down to $15 million before being delisted 18 months ago. In other words, this place could certainly be viewed as a steal, as much as it's possible to view a $7.35 million 4BR apartment as a steal. Could it become the second River House pad in almost two years to find a buyer?