Though Wheelguy's suggestion is an alternative it leaves you with a spare of a different size than the other tires.
There is no need to use a smaller tire for a spare.
Since my earlier post from 2006 I have upgraded to Michelin 180-15 XAS tires, which are slightly larger in both diameter and section than the earlier 175's I had successfully gotten into the space. The new spare fits as did its predecessor.
Though in that post I alluded to "prying" with wood sections I hesitated to share with the forum my actual methodology for enlarging the aperture for fear I would freak someone out. What I actually did--and this method has been used by some other esteemed 100 drivers since--is to insert a scissor jack into the space and, with pieces of wood above and below the jack, gently expanding the height so that a tire with a larger section will fit.
The method takes some nerve and patience. Go slowly as when applying force the car may sound like it is going to bend or break, but please trust me when I tell you that the sheet metal above the aperture--and not the rear deck--will give enough so that a tire can be slipped all the way into the cover just as the original bias tires did. You may want to slide the jack from left to right and back to make things conform equally.
Using a plastic laundry bag around the tire helps with insertion/withdrawal. Again, sometimes size does matter and this is one of those cases.
As to the little keeper device I simply put a heavy tie-wrap around one of the spokes and slip the end of the bar into the loop, then tighten down the back end with the strap. Everything will draw up tight and your spare will be secure.
Don't forget to fully inflate the spare--and check it every so often--so that it will be ready for use if needed.