After two days of agonizing delay over the particulars of the contract of swingman Mike Miller, a period during which it was speculated that the career 40.5% three-point shooter may have been backing off the idea of joining the Heat, Miller officially signed a five-year contract with the Miami Heat yesterday.

The Heat now has Chris Bosh, Dwyane Wade, Lebron James, Mike Miller and Udonis Haslem under contract.

The Miller used up just about every last dollar available to the team under the salary cap. Every contract added from this point forth will cause the Heat’s team salary to exceed the cap, and therefore rely upon an exception to execute.

There are two exceptions which the Heat can now utilize to acquire new roster players.

The first is via “Bird rights”.

This provision applies to the one, and only one, unsigned player to whom the Heat still retains Bird rights – Joel Anthony. This exception gives the Heat the ability to re-sign Joel to a contract as long as six years in length and as big as $103.0 million in value. Of course, that’s ridiculous. Joel will likely be back in South Florida, but at a much more reasonable contract which adequately reflects the value of his services.

The second is the minimum player salary exception.

Every player other than Joel whom the Heat acquires from this point forth throughout the off-season, whether he be the team’s second round draft pick from last month or whether he be a 20-year veteran, needs to fit within the confines of this provision.

Teams can utilize this exception sign players to minimum salary contracts, or trade for players with minimum salary contracts, when they are over the salary cap. Such contracts can be for up to two years in length. For two year contracts, the second season salary is the minimum salary for that season. The contract may not contain bonuses of any kind (as unrealized bonuses could lower the contract value below the NBA’s minimum wage, and realized bonuses could raise the contract to an amount that would no longer classify it as minimum).

Minimum salaries are based on a player’s tenure in the league. The minimum salaries scale upward each season. Here they are, by season:

So when you want to determine the maximum contract the Heat can provide to a player, you would look at his ESPN.com player profile to determine how many seasons he’s played in the NBA, and pull the appropriate figure from the chart above. For example, Matt Barnes has been in the league for seven seasons. He would therefore be eligible for a $1,146,337 contract next season. If he signed a two-year contract, the maximum length for a minimum contract, the second season (before which he would have eight years tenure) would be for $1,265,976, making for a two-year contract worth $2,412,313.

One last thing. When a player has been in the league for three or more seasons, and is playing under a minimum contract of one-year in length or shorter, the league actually reimburses the team for part of his salary – any amount above the minimum salary level for a two-year veteran. In such cases, only the two-year minimum salary is included in the team salary, not the player’s full salary. This is done so that teams won’t shy away from signing older veterans simply because they are more expensive when filling out their last few roster spots. It also means that you could see a lot of players with an $854,389 cap hit next season, but that doesn’t necessarily reflect the players’ true salaries.

There is no limit to the number of players that can be signed or acquired using this exception. In the pre-season, a team can carry as many as 20 players on its roster. Of course, by the start of the regular season, it needs to get down to the 15-player maximum. Oftentimes, teams will utilize this exception to offer unguaranteed contracts during the preseason, which can be terminated prior to the start of the season at no cost to the team. Rare are the circumstances when veteran players would accept being dangled like that; doing so is more commonly associated with rookies attempting to find a place in the league. However, Carlos Arroyo did so last year. Arroyo eventually made the team, and stayed with the club for the entire season.

Up next for the Heat will be the signings of Cavalier free-agent center Zydrunas Ilgauskas and Trail Blazer free-agent power forward Juwan Howard to minimum contracts. Each has more than ten years of NBA experience.

After Howard and Ilgauskas, among names already floated with potential interest by the Heat are outside free agents Brad Miller, Eddie House, Jason Williams, Jerry Stackhouse, Keyon Dooling, Kwame Brown, Matt Barnes and Rasual Butler. Free agent members of the 2009-10 Heat team who could be back for a curtain call include Carlos Arroyo, James Jones, Jamaal Magloire and Kenny Hasbrouck. Heat draft picks with a shot at making the big club include Da’Shaun Butler, Dexter Pittman, Jarvis Varnado, Patrick Beverley and Robert Dozier. Among the players with fully unguaranteed contracts, whom could be waived by their existing teams and subsequently picked up by the Heat, is Erick Dampier.

For a more complete list of available free agents, click on the Salary Cap tab above and click through to FreeAgents.