| Year | Title | - | Chart Positions | Chart Positions | Album |
| Year | Title | Irish Singles Chart | U.S. Modern Rock | UK Singles Chart | Album |
| 1986 | "Fear and Favour" | - | – | – | non-album single |
| 1988 | "Be Still" | - | – | – | non-album single |
| 1989 | "Arclight" | - | – | – | non-album single |
| 1990 | "Dronning Maud Land" | 6 | – | – | non-album single |
| 1990 | "Man Scared" | 17 | 20 | – | Twist |
| 1991 | "Arclight" | 7 | – | – | Twist |
| 1991 | "Twist" | 14 | – | – | Twist |
| 1991 | "Deborah" | 17 | – | – | Twist |
| 1993 | "Show of Myself" | - | – | - | Johnson |
| 1993 | "Drunkard Logic" | – | – | 56 | Johnson |
| 1993 | "World Exploding Touch" | - | - | - | Johnson |