Hedaya has played many flavorful character parts in features, often portraying cops ("The Hunger" 1983; "Tightrope" 1984; "Running Scared" 1986; "The Usual Suspects" 1995), crime figures, or crusty regular guys. His most indelible impression was made in "Blood Simple" (1984), the landmark independent feature debut of the Coen brothers. In a rare substantial role, Hedaya was Marty, the cuckolded husband who hires a sleazy detective to kill his unfaithful wife and her lover. In this unsympathetic but strangely poignant characterization, the actor's sloped nose and ample jowls take on a haunting Nixonian quality. Hedaya continued to demonstrate his prowess in six features in 1993 including "Searching for Bobby Fischer" as the tournament director, and "Mr. Wonderful" as a buddy of working class hero Matt Dillon.

Hedaya did very little film work the following year--just a supporting role in "Maverick" (1994)--opting to devote more time to TV, playing a bail bondsman in three syndicated telefilms derived from the 1988 feature "Midnight Run". He began making up for lost time in 1995 with character turns in several high-profile features including "To Die For", "Nixon" and "Clueless". The latter was a sleeper teen satire which cast Hedaya in the atypical role of a well-to-do lawyer raising a fashion-conscious daughter on his own. He also found time to appear in two ambitious dramatic anthology series on cable, "Fallen Angels" and "Picture Windows" (both Showtime, 1995).

The actor continued to remain busy in 1996: he was Bette Midler's ex-husband in the hit "The First Wives Club", appeared as Robert De Niro's brother in "Marvin's Room", and was featured in the ensembles of Ron Howard's "Ransom" (with Mel Gibson and Rene Russo) and "Daylight" (alongside Sylvester Stallone).