At the time of writing the app, which was released in Canada last month but is now available elsewhere, has a score of just one-and-a-half stars, with those leaving bad reviews all focusing on the game's similarity to Nimblebit's resource management sim.
"If you are going to get this game then you are playing a game that has been copied," one user, Planopink, writes. "Tacky rip-off merchants," adds Miellies. "Go Tiny Tower!"
"This is just a pure rip-off of Tiny Tower," says david171, "and it's nowhere near as fun. I got bored in a few minutes. As with the rest of Zynga games there is no Game Center integration so I can't even connect to my friends on there.
"Download Tiny Tower instead and support that game, this is just poor."
Another, Dr Crevice, calls on users to bombard the app with negative reviews. "This game is a carbon copy of Nimblebit's Tiny Tower," he writes. "Download it, post a one-star review and file an app report with Apple, and tell others why you've done this.
"It's time to send Zynga a clear message that leeching off other people's hard work isn't acceptable."
Late last month three-man indie studio Nimblebit, whose Tiny Tower Apple named US iPhone game of 2011, pointed out the striking resemblance Dream Heights bears to their game. Zynga, however, denied it, with CEO Mark Pincus reeling off a list of games that also featured towers – an argument we picked apart.