Look at Twilight2000 V2.2 (not the original). It is based on 1D20 with a ROLL UNDER mechanic. To determine a Skill you add a Skill Level (rated from 1 to 10) to a Characteristic Score (also rated from 1 to 10) to get an Average Chance of Success with that skill. Initiative is rated from 1 to 7 with high score going first. Hit points are generous so death won't be immediate. The game is available at Far Future Enterprises and it plays fairly smoothly. I have had to make only a couple of changes to run my Mercenary campaign. They are...
Skill Difficulty Chances are NOW based on Traveller's Difficulties:
Average Skill Level (Characteristic + Skill Level = SKILL or a 10 for a perfectly average character with a 5 Skill and a 5 Characteristic)
Easy Skill Level (SKILL X 2 or a 20 for the character above)
Routine Skill Level (SKILL X 1.5 or a 15 for the character above)
Difficult Skill Level (SKILL X 0.5 or a 5 for the character above)
Formidable Skill Level (SKILL X 0.25 or a 3 for the character above)
Impossible Skill Level (SKILL X 0.1 or a 1 for the character above)
You record these Skill Levels and then just "shift" the Difficulty Level for things like target obscured, shooter's wound level/fatigue, or movement during play. This makes skill resolution very fast and fairly easy.
The second change I make is to Initiative. I like a randomized initiative so I have my characters roll 1D6, add this to their INITIATIVE SCORE. I then divide this score by 2 (round up) and this is the number of ACTIONS that character can take in that round. These actions include reloading, firing and movement. The average initiative in this system is 3 Actions.
Just remember that you need Version 2.2's PDF. The earlier version was more complex.