You'll never remove the sediment at the bottom when bottle conditioning. 5-6mm is not a terribly large amount of sediment either.
Here are a few methods that can reduce the sediment:
Use a secondary fermentor, typically a 5-gallon carboy. This is used after primary fermentation, and has little to do with fermentation despite the name. It removes the beer from the yeast cake (trub) and therefore lots of sediment. A secondary is also great for dry-hopping if you're doing that for this IPA. 1-2 weeks in the secondary is an acceptable amount of time, but longer is totally fine too.
Cold crash if you can. This is most effectively done in a fridge for the last few days to cause the yeast to suspend itself to the bottom of your fermentor. I've had luck by placing my secondary in a large container of ice for 2 days and racking into my bottling bucket without moving it, but the amount of ice used and difficulty racking wasn't exactly worth it.
Perhaps a "no brainer", but great caution should be taken to not disturb the sediment before racking to your bottling bucket. I like to place my fermentor on the counter I'll rack from a few days before the actual transfer.
You can also use several fining methods/agents to help reduce the sediment, but it is moreso to ensure a clear (as opposed to cloudy) beer:
Whirlfloc/Irish Moss - Used in the last few minutes of the boil, it helps weigh down sediment in your primary fermentation.
Gelatin - Used in the last few days before bottling, it is often used in conjunction with cold crashing. This might not be the best option as it can pull much of the hop flavor and aroma out of the beer.
With any of these methods, it's important to note that there will be enough yeast to carbonate. However, the more sediment you separate from the beer using these methods, the longer it will take to carbonate. I've had beers carbonate fully in 2 weeks when using none of the aforementioned methods, but the beers I've cold-crashed with gelatin took 6 weeks to fully carbonate.