Awards
| Year | Award | Category | Movie | Result |
|---|---|---|---|---|
| 1991 | Independent Spirit Awards | Best Actor | My Own Private Idaho | Won |
| 1991 | Venice International Film Festival | Volpi Cup for Best Actor | My Own Private Idaho | Won |
| 1990 | National Society of Film Critics | Best Actor | My Own Private Idaho | Won |
| 1988 | Academy Awards | Best Supporting Actor | Running on Empty (1988) | Nominated |
| 1988 | Golden Globes | Best Performance by an Actor in a Supporting Role in a Motion Picture | Running on Empty (1988) | Nominated |
| 1988 | National Board of Review | Best Supporting Actor | Running on Empty (1988) | Won |
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