Re Sveshnikov's 'more sensible is Bronstein chess', I believe that he is referring to the variant of shuffle chess where the two players take turns placing the pieces on the back rank. I've never investigated this idea and it would make a good start point for a followup post.
This is confirmed in the Telegraph's 2006 obituary of David Bronstein.
He was one of the originators of Rapid Chess played at a faster time limit, with 30 minutes or less for the game, and developed a form of Random Chess well before Bobby Fischer claimed ownership of the concept. In Bronstein Random Chess the pawns are set out and the first eight moves involve placing the pieces on the vacant back rank.
HarryO pursued this idea in a comment to the Modern Chess post, where he proposed that the players alternate placing the King, Queen, etc. until all pieces have been placed. While this is certainly an easy method to follow, it has the drawback that it can favor certain of the 960 possible positions. We have already seen this problem in the method used to select start positions during last year's 'Kings and Queens' event in St.Louis; see the comment to The Chess960 Wheel of Fortune.
Since the only method to ensure an even chance of choosing all positions is to start by placing the Bishops, and since the position of the King and Rooks is determined by the start squares of the other five pieces, I propose a different method.
Player A places a Bishop, which the other player echoes.
- Player B places a Bishop on a different color square than used in the previous step, also echoed.
This leaves the Queen and Knights to be placed. I propose that the two Knights be placed on the same step by the same player, and that this should be considered a single step.
Player A places either the Queen or the two Knights, which the other player echoes. The choice of placing either the Queen or the Knights is Player A's decision, as is the choice of square(s) for the piece(s).
Player B places the remaining piece(s) -- either the Queen or the two Knights -- also echoed.
- The King and Rooks are placed on the three remaining empty squares according to the rules of chess960, the King between the Rooks.
This method ensures that all 960 positions have an equal chance of being selected. It also allows for the development of a new kind of opening theory. As for the question of which player gets to go first as Player A, that can be decided using the same sort of method that we already use to determine who plays White.
[To be consistent with the standards of this blog, I should have titled this post 'Non-random Chess960', but the play on words was too cute to ignore.]