I've read a couple books on soils recently that challenge the notion of adding lots of compost to the soil. Both of them recommend adding far less compost than most organic gardeners (me included) typically use.
For instance, for a new garden that has low organic matter, Phil Nauta, in Building Soils Naturally, uses 2-3 inches mixed into the top 8-10 inches of soil. But he says that's too much to use more than once. For established gardens, he adds 1/8 to 1/4 inches of compost to the surface and, at most, may "lightly incorporate" it -- no tilling.
If your soil is heavily compacted in the spring, that calls for either a substantial layer of mulch to protect the soil over the winter, or else (if your climate permits) a cover crop. In urban and suburban areas, mulch is available free from tree trimmers. I'd use at least a 4-6 inch layer. In rural areas, you may be able to get horse manure (test it first) -- it can be piled as high as 12 inches and will shrink to half of that by spring. One year I had access to horse manure from an organic farm and covered a couple beds at least a foot deep. In the spring it wasn't all broken down, but it was good enough for tomatoes.
If you still have a month or so before you will be planting in that compacted soil, you can make the soil more workable simply by mulching with whatever you can find. Google "lasagna gardening" for ideas.
Another longer-term strategy is to plant crops that will help loosen the soil, such as daikon.