Here's a delightful little gumdrop from 1991 in which a detective agency and rock band (not two seperate entities, BTW) deal with a kidnapping. It looks pretty good.
This was an early work of character designer Goto Takayuki. He is mostly known for his character design work: Video Girl Ai and Please Save My Earth (one of my all-time favorites) are two examples, and he has been animation director for a long list of other shows. But this, and The Samurai (another title I recommend) seem to be the only titles where he is credited as "director."