The craziest wave of free agency is in the books, as most teams have completed their strongest open-market push to position themselves for the 2013 season.

The Patriots have spent the majority of their cap space, most notably by retaining cornerbacks Aqib Talib and Kyle Arrington, and adding wide receiver Danny Amendola and safety Adrian Wilson. The Pats entered free agency with $25 million in cap room, and it’s hard to perfectly quantify how much they’ve got remaining because not all contracts have been filed with the NFLPA just yet. An educated guess here is that they have $9 million left to spend. Keep in mind they’ll need to save $4-5 million for draft picks, so the heavy work is done.

With that in mind, the Pats have addressed some needs but have some areas that still need to be addressed.

What’s done:

L Shored up secondary: The Patriots liked their secondary’s progress after the Talib trade, and they’ve decided to give that group another run. Talib will man the left side with Alfonzo Dennard at right corner if he is available, and Arrington will slide into the slot. This also ensures Devin McCourty will remain at safety, and he could have a new right-hand man with Wilson joining the mix. Wilson is a strong leader and an intimidating presence who will improve the middle of the field. The Patriots have done their best work in free agency in this area.

L Proven willingness to improve: All was quiet at the dawn of free agency, then Wes Welker signed with the Broncos. Things intensified at the end of the week when the Patriots hosted defensive ends John Abraham and Dwight Freeney and wide receiver Emmanuel Sanders, plus the flurry of signings. Even though the Pats followed their standard model of not aggressively targeting the highest-profile players, they’ve been in on other big names who can help the team.

L Sparked return game: The Patriots’ pedestrian kick return game got a boost when they signed Leon Washington. Since 2007, when Washington became a full-time returner, his average of 26.2 yards per kick return is the fourth best in the NFL among players with at least 100 returns. Meanwhile, the Pats have been in the bottom quarter of the league in that category in the last two seasons. The Patriots visited the end zone more than any team in the league in 2012, despite a heightened degree of difficulty with their starting point.

What’s left to do:

L Reinforce the receivers: Replacing Welker with Amendola is a step back, and releasing Brandon Lloyd means they’re starting from scratch. Not a single receiver under contract caught a pass in a Patriots uniform last season. The Pats could increase the talent level by targeting free agents such as Emmanuel Sanders, Darrius Heyward-Bey or Kevin Walter, re-signing Deion Branch, Donte Stallworth or Julian Edelman, or identifying talent in the draft.

L Find a right tackle: It seems unlikely that Sebastian Vollmer will sign anywhere until Jake Long sets the market with his decision, but if the Pats lose Vollmer, it’s unclear which direction they’ll turn. Someone like Eric Winston would make sense if the Patriots don’t want to go all-in on Marcus Cannon, or they could tap into a very deep draft pool, which should extend well into the middle rounds.

L Add pass-rushing depth: Defensive ends are affordable, similar to the cornerback market, as proven by Cliff Avril’s two-year, $15 million contract. That’s why the Patriots have explored so many options, and Abraham, Freeney, Osi Umenyiora and Elvis Dumervil are still out there. An additional pass rusher isn’t absolutely essential because the Pats like their youth behind Chandler Jones and Rob Ninkovich, but the value might be too good to pass up at such an important position.