I love the concept of 13th Age, to take the Pathfinder/d20 System and simplify it, adding some more role-playing elements. But there is a lot of the execution of the game that I just hate. Biggest of all, I hate the meta-gaming system of abilities that are available on an arbitrary schedule: At-Will, Once Per Battle, have a Chance to Recharge after the battle, or Once Per Day. That breaks the player out of the character's head and hurts the immersion of the game.
In our last adventure we decided to try something different with the Animal Companion system. In 13th Age you can either buy an Animal Companion who is always by your side, or a limited companion who is only available every other battle. Instead of that, because I don't understand why you would not summon aid in every battle if it was possible (and there's no good reason for why it is only possible half the time), we tried a new system. For our Ranger who had the limited Animal Companion I had her roll a d6 at the start of every battle, her companion arrived on the turn when the escalation die equaled the number rolled. It got the normal move and standard actions, and always started at the edge of the battlefield.
This seemed to work pretty well, some battles were fast enough the companion didn't arrive. At the least the companion didn't arrive until the second round, and it always needed to move into position, so it was not as convenient as having the constant companion. It seemed to be a good comprimise between not always being there but not being completely unavailable.
Best of all, I could easily define and describe it - the Ranger had to call for an animal, and there was no way of knowing just how close the appropriate type of animal could be to the battle (she only summoned canines, thanks to the murdered ghost of her pet- something that tied into her One Unique Thing). That gives the delay a reasonable explanation from a role-playing standpoint, and makes it a lot better in my opinion. We only tried it for one game, but it seemed to go well so I think we'll keep it as our new system.