Eliminating chainslap on a 90's Stumpjumper I have a mountain bike - a Stumpjumper hardtail frame with a Shimano drivetrain - where I'm getting a good amount of chainslap. Before I start fiddling with stuff, I'd like to understand the problem better. 

This is a new-to-me bike that's only recently been built from a mix of old and new parts. 




(I've put up more pictures of the bike here, but these are the two that most clearly show the drivetrain.) 

I believe I have two options here: 


Increase the tension on the chain (somehow), or 
Pull links out of the chain until all is well. 


What are the advantages and disadvantages of both? Or are there other strategies I'm missing? Or is my time better served by simply wrapping the chainstay and living with the problem? 

(While this isn't strictly relevant, I'd be remiss if I didn't point out that the front derailer also has issues - I can't get enough cable tension to get the chain to shift into the big ring up front.)
Let me introduce you to the B-Screw...

Look at how that derailleur is hanging. The parallelogram is angled skywards rather than downwards. This is because the B-Screw at the back of the derailleur is not screwed in enough. This screw contacts the derailleur hanger's little 'spur' and you may want to twist the derailleur body clockwise to make it easier to do up the screw. Tighten it all the way, then go into the big cog and back it out so that the top pulley is close but not touching the sprocket. This will put the B-Screw in its correct position, putting a sensible amount of tension on the chain.

As for your front derailleur not making it onto the big cog, the problem may be with the bottom bracket. These come in different lengths and if the cranks or b/b have been repaired/upgraded over the last decade, due concern for the chainline may not have been given. Take out the one that is in there and put in a cartridge b/b of the same shell size with a shorter length. The next size down may be all you need but, without seeing the gap between the cranks and the chain stays I can only guess. Obviously you want the cranks to be an equal distance from the chain stays on each side with enough room in there for the triple chainset. the derailleur (front) will probably need adjusting by then, this has the outer plate parallel with the chainring and 1mm above the outer chainring teeth.

To make the bike look really good and eliminate chain slap problems in style, consider going on eBay to get a genuine Shimano 'Shark's Fin':