Historical Fact: Gerrymandering Invented by Democrats

 Elbridge Gerry (1744-1814) was a Democrat.  Gerrymandering was first used in Massachussets in 1812 by the Democratic-Republican Governor, Elbridge Gerry to keep the State Senate in his party's control even though Gerry himself lost the 1812 election for governor.  The Democratic-Republican party became the Democratic party.

Obviously, after the Democrats showed how effective gerrymandering is, Republicans began using the tactic too.

Since both sides have used gerrymandering for a very long time, it's unlikely that the system will change.

Control Gerrymandering with the Mathematical Meaning of Compact

Compact and contiguous are both terms with mathematical definitions. Compact means that a line drawn between any two points in the district does not leave the district. Contiguous means connecting without a break, in other words no islands. If these definitions were enforced by the courts, gerrymandering would be a lot harder to do. My Congressional district was drawn to look like a Thompson submachine gun. It was not compact by mathematical definition, but was legal by current case law. I believe clarifying the meaning of compact to be the mathematical definition is the easiest and most practical way to control gerrymandering. 
 
Exceptions could be made for coastlines and physical, as opposed to political, islands. Obviously, state borders are OK as district boundaries no matter how convoluted they are. However, rivers that are internal to a state open up gerrymandering possibilities. Defining a river allows all sorts of abuse. As an example, the navigable waters of the US became any mud puddle in your back yard after the EPA got through interpreting the law.  
 
Perhaps exceptions could be based on the existing road network instead. If two places are physically close, but you have to drive 100 miles in a roundabout fashion to travel from one to the other, then they shouldn't have to be in the same district. For example, the Grand Canyon should be OK as a district border. At this point it gets tricky, but maybe the law should say that contiguous points excluded from a district must be further away by road than any points included in the district.

http://www.washingtonpost.com/opinions/two-reading-lessons-from-the-supreme-court/2015/02/27/abcae45e-bde3-11e4-bdfa-b8e8f594e6ee_story.html