Why not allow U.S. Congressional districts to overlap two or more states? Surely people living along state lines will often share geopolitical interests with people living in the bordering state(s)?
For example, currently:
The MO-3 district is held by a Democrat, but the IL-17 district is held by a Republican. Both districts represent portions of the St. Louis metropolitan statistical area. (Not the best example, because the IL-17 district is badly gerrymandered, but still accurate.)
The TN-9 district is held by a Democrat, but the MS-1 district is held by a Republican. Both districts represent portions of the Memphis metropolitan statistical area.
The IN-9 district is held by a Republican, but the KY-3 district is held by a Democrat. Both districts represent portions of the Louisville metropolitan statistical area.
The SC-2 district is held by a Republican, but the GA-12 district is held by a Democrat. Both districts represent portions of the Augusta metropolitan statistical area.
Etc., etc., etc. And I didn't even consider bordering districts which have representatives from the same party but who hold somewhat different positions on specific issues.
Pros: Again, this would allow natural communities that happen to straddle state lines the chance to seek more unified Congressional representation. Also, this would reduce (although not eliminate) the discrepancy between the relative representation for individuals in each state. For example, currently, some states have a population-to-representative ratio of more than 800,000 to 1, while others have a ratio below 600,000 to 1. This system could help even out those discrepancies (excluding, perhaps, Alaska and Hawaii).
Cons: Mainly, this would be difficult for the states in question, because their legislatures would both have to agree on the redistricting plans. Also, as far as I can tell, this system would probably require a Constitutional amendment, not simply a statutory law.
Yet to be determined: I'm not sure how this would affect redistricting concerns. This kind of system may lead to more "packing" schemes, but it's not as though the current system doesn't allow for "packing" or "splitting" of cities along the border, too.