Almost as important as tuning is hammer voicing. The hammer is the felt object which strikes the string to produce a tone.Depending on the condition of the piano, the piano may sound too loud, too bright, and too harsh. Another hammer issue can be unevenness from one note to the next. This happens because most players play certain notes more than others. The more often played notes get louder than the ones less often played.
The remedy for this situation is called hammer voicing. It is done by filing off a layer of the hammer or altering the density of the hammer with a voicing tool. Voicing is relatively inexpensive or in some cases minor voicing is included in the price of the tuning.
As a pianist of both classical and popular music, I have a hands-on understanding of the variable tones which can be created and improved upon.