The Rock & Roll Hall of Fame’s history with ‘80s new wave acts has been inconsistent and, at times, downright head-scratching.

Several of the genre’s biggest artists have now been inducted, but there’s seemingly been no rhyme or reason as to how long they’ve had to wait. Talking Heads got the Hall call in the first year they were eligible, while it took the Cure 15 years to receive enshrinement. Depeche Mode needed three nominations to finally garner induction, while Duran Duran only required one nom to secure their place in the Hall (albeit, 15 years after they were first eligible).

Though the Rock & Roll Hall of Fame has (eventually) done right by these artists — including other new wave greats like the Police, Blondie, Elvis Costello and the Cars — many other deserving new wave greats remain on the outside looking in. We’ve highlighted the five most egregious omissions in the gallery below.

READ MORE: 20 Greatest New Wave Bands

Our list includes Grammy winners, multi-platinum stars, era-defining groups and some of the biggest hitmakers in music history. A couple of these artists have received Hall of Fame nominations in the past, only to fall short of induction. The others remain confoundingly out of the conversation entirely, much to the chagrin of their fans.

We start with a band – really bands (plural), if you want to get technical – that may not be on this list for long, considering they’re a nominee for this year’s class.

New Wave Bands That Belong in the Rock and Roll Hall of Fame