As Alex noted in his last post about CJ Watson and the PG market, the Bulls do not have a lot of available ways to sign free agents. Being over the salary cap in nearly every conceivable scenario, cap exceptions are the only way to take on more money.
Here are the two main ones the Bulls have at their disposal:
Mid-Level Exception (MLE) - can be used for a $5m starting salary, for up to a 4-year deal. The Bulls used this when they signed Richard Hamilton last offseason, but it can be used every offseason. It can also be split amongst several players.
Bi-Annual Exception (BAE) - for up to a 2-year deal, starting at $1.9m. As indicated in its name, this exception can't be used two years in a row. The Bulls did not use it last offseason, so they can do so in this one.
There are other 'exceptions' that make the salary cap the soft gooey forgiving entity it is: They can sign their first-round picks to the rookie scale. They can sign players to the minimum salary. Even the rights to re-sign Omer Asik as a restricted free agent is technically an 'exception'.
Another way for the Bulls to take on extra salary while being over the cap is through trades, as there's an exception (though rarely named as such) that you can take in more salary than you trade out. This used to be 125% in the old CBA, but that rule has changed a bit:
|Outgoing Salary||Maximum Incoming Salary|
|< $9.8m||150% of incoming + $100k|
$9.8m -> $19.6m
|incoming + $5m|
|> $19.6m||125% of incoming + $100k|
So the Bulls could, hypothetically, take the non-guaranteed contracts of Brewer and Korver, and deal them for a player making $14.155m.
Or could they? As mentioned in the earlier post about the Luxury Tax, the available exceptions change if you're over that tax threshold. If that mentioned trade would put the Bulls over the tax, then their potential incoming salary is lowered to the amount seen above highest-money trades, in this example down to $11.1825m.
That's not a huge difference, but there are other ways the exceptions are now limited if you're over the tax line (specifically, if the move puts you $4m over, but that's enough to keep you from using the full MLE).
BAE cannot be used.
Beyond the above mentioned restrictions in taking on salary in a trade, starting next offseason a taxpayer can not trade for a free agent in a sign-and-trade. This is a bit of a break for OJ Mayo fans, as this wouldn't even be an option if this rule wasn't eased in.
More than ever, the tax matters. The Bulls are bumping right against that line, to the point where they literally can't bring everyone back without going over. And if they're over, the limited options to acquire players gets even smaller. That's why it's only somewhat-absurd to suggest the Bulls could be looking at the likes of Jannero Pargo and Tracy McGrady: if you have only the 'mini'-MLE, and the ability to sign players to the minimum, the caliber of available players will drop.