You can customise the amount of magic available in the game in several ways:
Start out all magic at limited effect instead of standard effect will dramatically reduce most magic while leaving more powerful magic still possible. It will force magic users to use mana burnout or stress on most spells, dramatically reducing the availability of magic.
For an entirely different feeling, you can make rituals mandatory and rule that only magical creatures can use magic without rituals. This way, magic can still be powerful (remember that rituals grant a +1 to effect) but cannot be used in combat or other action scenes.