If I choose 4 damage counters on my Pokemon with Espeon's "Solar Suggestion" attack, can I then place 3 or fewer damage counters on my opponent's Pokemon?
No, you can't. You must place the same number of damage counters on your opponent's Pokemon as you removed from your own Pokemon.
Source: Undaunted FAQ (2010-09-09), PUI Rules Team (2010-09-09)

Relevant cards

Note: All applicable cards may not be listed below.
COL1_4
HGSS3_2