Don't let de-ionised water near your car (except in the battery) - chemical engineers call it the 'universal solvent' as it will scavenge its lost Ions (electrically positive charged particles) back from any material (especially metals) that it comes into contact with. Systems that use DI water are designed with great care, and cannot contain metals normally found in a car engine (aluminium, copper, steel and brass) - some electronic and electrical cooling systems use DI water because it does not conduct electricity, but these systems are designed for DI. Chemists use DI water because they are pretty sure it will not contain unwanted chemicals and upset their experiments.
I would use a premixed 50/50 solution of universal OAT or HOAT (slicate free) Halfords do a 5 litre universal one, I use it in my motorbikes and cars - I just drain whatever would come out from the normal tap in bottom of radiator (about half the system quantity) and top it up with 50/50 premix, then run the car for a week and do the same (this way you will replace at least 75% of coolant), keep your eye on the radiator level for a while after both procedures and top up if needed, I have never bothered draining and refilling the expansion bottle (you either need to remove the battery or go under the car to remover the bottle). If you want you can suck out the fluid from bottle with a siphon thing (available from home-brew shops) and refill to halfway between max and min level.
Remember the ethylene glycol anti-freeze bit does not lose effectiveness over time, all you are doing is making sure the corrosion inhibitors (which do get used up) are being replenished.
Its a pity that the Jazz doesn't have a proper temperature gauge because the first sign that you have an airlock in the cooling system is the temperature gauge goes a lot higher than normal.
if your heater does not work very well after the coolant change you will probably have an airlock in the heater circuit. Try to do the drain and refill with front of car higher than the rear (if you put front wheels up on ramps it also enables you to get access to coolant expansion bottle from under the car) as this allows air to come out easier.