I'm not in favor of doing this, necessarily, but due to the number of players that have been offered on the trade block, only to be forced off because the 60-day wait happens a few days after the trade deadline, I think it's worth opening up for discussion.
This proposal would do away with the 60-day trade restriction rule entirely, including both off-season signings and trades. If a player is under contract for your team, regardless of when you acquired him (off-season FA, just traded for him, whatever), you can trade him at any time prior to the trade deadline. No more waiting for 60 days to expire.
Note: This proposal does NOT apply to RFAs. You would still have to wait one year after signing/matching to trade them.