Why each team makes the trade:
Miami - They swap a disgruntled Butler for a younger offensive small forward in Ingram and pick up a young 3 and D Heat culture guy in Nesmith. This keeps them competitive now and into the future.
New Orleans - Swapping Ingram for Butler makes New Orleans a legitimate contender. Yes they lose Jones, but adding Andrew Nembhard to a backcourt that just brought in Dejounte Murray is a coup. Nembhard and Murray are both terrific 2-way point guards who can also play off-ball. Butler makes up for the drop in wing defense lost losing Jones.
Indiana - losing Nembhard hurts, but this gives them an upgrade in size on the wing defensively in Jones. The protected first from Miami makes up for the fact they are losing 2 solid young prospects. This move also opens up cap for them going into next season.