The difference in depth prior to applying finishing coats should be no more than 1-2mm.
So if 3/8 inch it will need filling out to level.
If the wall is painted remove any dry flaky paint, also give the surface a little sand down to help with adhesion.
I would go for a
bonding coat to fill in low areas.
Then let this start to set, the painted areas of the wall will need to be primed with PVA. The PVA should be left to dry then a second coat of PVA left to go tacky prior to finishing coats being applied.
You need to use
multi-finish on base coats.
Two applications of of multi:
First coat spread evenly over wall at 2mm depth, this does not have to be perfect, as you will it leave a short while to take to wall (5 mins should be long enough but in this time you can be preparing for your second mix, cleaning buckets and tools etc..). Then flatten out using trowel at about 30-35 degree angle, adding to any low spots. I work from top to bottom.
Once flattened then mix a second slightly wetter the the first, again apply an even coat but about 1mm in depth, leave a short while to take then flatten out again as before, this time to avoid lines and low points. This can then be left until it starts to stiffen up a finger test should be done, if your finger does not leave an impression, you can the do a wet trowel.
Dampen wall down with water using either a fine spray or brush (flicked on with brush, rather than painted on)
Then you can start to smooth the wall down again trowel at 30-35 degrees.
This should bring out any lines/imperfections. If still have still low points at this stage, don't use the fat brought up be the wet trowel but use a little of the stuff you have left over from the second mix. If not the plaster finish in that area may dry powdery and becomes hard to paint.
Always use clean water and keep your tools clean.
