Tiling outside - how thin can cement mortar be laid?

[Araucaria]

I've got a medium-sized concrete slab to tile - about 4m by 5m. The tiles that are going on are limestone, 15mm thick, and 30cm x 30cm.

I'd like to use a simple cement (or cement + lime) mortar to bed the tiles - I've done other areas with this and it seems to have worked well (two years on and the tiles are all still stuck down). But I have given myself a problem - I failed to get the concrete slab level and it's slightly higher in the centre than at the edges - a couple of centimeters difference. I'd like the tiled surface to be pretty well flat, partly for the appearance, and partly because I don't want rainwater flowing into my house, so whatever I use as an adhesive is going to need to be thinner in the middle of the tiled area.

At the edges I can get about 30mm thickness of adhesive, and I think this might just about be OK for a cement mortar. There's about 60cm - two tiles-worth - all round the edges of the slab where this is possible. But in the middle it'll be more like 10mm and there I'll probably have to use a relatively expensive adhesive - elsewhere I've used Carrosouple HP and this seems pretty good.

Does anyone know how thin a mortar bed can be for laying outdoor tiles? I'd like to use as much mortar and as little "proper" adhesive as I can, as the Carrosouple is quite expensive and it'll need quite a bit. The slab slopes gradually up fro the edges to the middle so I need to fix the point at which I change from one product to the other.

Can anyone help please?