how do I level and strengthen loft joists

[mishmash85]

I'll be insulating and boarding part of my loft for storage only.

I'd like to strengthen the joists and make it level.
I'm happy just to level the "boarded area."

What's the best way to do this?
Add noggins to stiffen the current joists?
Sister timber along side the current joists? What size?
Should I strengthen just the area to be boarded or the entire length of the joist?
Or screw timber on top of the joists perpendicular to them?

I've read lots of different information and I'm more confused.

The joists are 37x75mm and span 4.5m, they are no where near level.

I've attached a little diagram showing some rough measurements of the area I want boarded

 

[Bonni]

I would fit the appropriate size timbers/steel etc.. to the locations specified by the structural engineer.

 

[cdbe]

A lot depends on what you can physically get in.