There are shades of 30 Rock and Unbreakable Kimmy Schmidt in this hilarious show about a one-hit-wonder girl band reuniting after 30 years. No wonder, given it’s by Tina Fey and Robert Carlock

If you didn’t know beforehand, it would not be long before you realised that Girls5Eva (Sky, Now) came from the school of Tina Fey and Robert Carlock, who gave us those perennial delights, 30 Rock and Unbreakable Kimmy Schmidt. The new show, about a manufactured 1990s girlband of the same name (“We’ve been best friends ever since we auditioned for a man in a New Jersey hotel room!”), is the brainchild of Kimmy writer and producer Meredith Scardino, in collaboration with Fey and Carlock. It provides a similar cocktail of laughs. There are parodies (this time mostly of music videos rather than TV shows or characters), “proper” jokes so densely packed you’re still unearthing more on third and fourth viewings, call backs, and throwaway gags so good they would be revered treasures anywhere else. The chemistry among its leads recalls – even if it doesn’t quite get there, because nothing can or will – the chemistry between Ellie Kemper and Titus Burgess in Unbreakable Kimmy Schmidt. In short, it is a joy.

Under the aegis of their sleazy manager Larry, Girls5Eva had one hit (Famous 5Eva) three decades ago but fell into obscurity after their follow-up tanked. It was called Quit Flying Planes at My Heart and was released on 10 September 2001. Since then, one of the girls has died (Ashley – “The one who got us all through our breakups with Moby”) and the remaining four members have drifted apart. We first meet Dawn (Sara Bareilles) as she is listening to the radio while having a mammogram. She has the perfect breasts for it, her doctor says – “Already so smooshed!” The Fey spirit, unable to know of a physical female indignity without leaping to embrace it for comic effect, remains strong throughout. Dawn herself is the mother-figure of the group. Always the responsible one then, she is now married with one child, constantly stressed (“Fireworks or terrorism?” she shouts when woken by a strange noise at night), and works long hours at her idiot brother’s restaurant (Dean Winters, essentially reprising his 30 Rock Dennis Duffy role). Hearing Famous 5Eva sampled as part of hit rapper Li’l Stinker’s latest moneymaker, she goes to pick up her royalty cheque from Larry and is coaxed into delivering the rest to her former bandmates, too.