This has less than 1% chance of happening, but since it seems everyone else has a dream scenario, I might as well give you mine. I think all of these trades are fair and actually could go down if certain things lead up to the picks. Obviously I would not trade down if Julio is on the board...
With the 10th pick the Washington Redskins select - Julio Jones
With the 11th pick the Houston Texans select - Aldon Smith
With the 12th pick the Minnesota Vikings select - Corey Liuget
With the 13th pick the Detroit Lions select - Prince Amukamara
If those 4 picks occur:
The Rams are on the clock, but unfortunately all of their favorite prospects have been taken. Bowers's knee doesn't check out, they don't like Kerrigan, and they believe it's too early to draft Pouncey or Ingram. WalterFootball thinks the Eagles love Jimmy Smith, so they trade up to get him.
Rams trade the No. 14 pick (1,100 points) to the Eagles for Nos. 23 (760) and 54 (360)
The Rams are now on the clock again, but unfortunately their favorite prospects have been taken. Ingram and Pouncey are gone and they believe they can nab Austin later. The Patriots see a great offensive lineman still available so they propose a trade to the Rams.
Rams trade the No. 23 pick (760 points) to the Patriots for Nos. 33 (580) and 74 (220)
It's been assumed that the 1st pick on day 2 has great value and it proves to be true. John Elway sees his guy at QB but he needs to jump ahead of the Bills and the Bengals because it looks like they are going to draft a QB after passing on them in the 1st round. The Rams have a player in mind but they think they can get him 3 picks later.
Rams trade the Nos. 33 pick (580 points) and 78 (200) to the Broncos for Nos. 36 (540), 67 (255), 186 (17)
The Rams now have a ton of picks which is great for a team that is still rebuilding.
2nd 36th DT Marvin Austin
The Rams have wanted this disruptive DT the whole draft and their previous trades have put them in a great position to select him.
2nd 47th RB Mikel Leshoure
Leshoure loves Jackson's style of play and he would love to learn from him. The Rams obviously need a successor sooner or later to Steven and Leshoure is the perfect fit.
2nd 54th CB/FS Aaron Williams
A great value pick here. Williams stated that he played a ton of Nickel while at Texas in the Game Changers film on NFL network. He can also line up at FS. Both of these positions are needs for the Rams so he is a great fit.
3rd 67th OG Marcus Cannon
I do not know much about this guy, but what I do know is that the Rams need a RG, Cannon is massive and intimidating also from the Game Changers film, and that Jason Smith and him make one huge right side.
3rd 74th WLB Mason Foster
The Rams need a starting weakside linebacker and they need someone who wants to rack up the tackles like JL55.. Mason Foster fits the bill
4th 112th RB Taiwan Jones
This guy probably gets selected by Oakland in the 1st round...even though they dont have a 1st round pick they will find a way to land him. But if the Raiders don't over value him, you can't pas up on a guy that runs in the 4.2s.
5th 145th FS Deunta Williams
The Rams need a safety and I am assuming this guy is pretty good considering he was on UNC's defense.
6th 186th QB Greg McElroy
I think he will become a great back up QB. Backup QBs need to just know how to manage the game and not do anything that hurts the team. With McElroy's Wonderlic score, he seems pretty smart.
7th FB Stanley Havili
McDaniels' offense calls for a FB that can block on 3rd down, can handle the ball, and can also catch. Havili does all of that.
7th SLB Mike Mohamed
I put this guy in here after reading an earlier post by mcihaelT. Credit to him