I think I'll have to disagree with Gabez here. The whole idea of the Cup is to pit your side against other teams of all sorts of levels and quality.

What they could do is take a leaf out of the English FA Cup system:

When a minnow team starts out at the 1st Qualifying Round, they're playing against teams from their local area, and of a +/- 1 Level. As they proceed, the higher level teams join in at about the 3rd Qualifying Round and they all go until the end of the Qualifying Rounds and then the League teams pitch in at the 1st Round proper, and then the gloves are off.

So, for example a Western League Premier team (Level 9 in the Pyramid) could play a team from their own division or the Western League Division 1 (Level 10) or Southern League Division 1 (Level 8) in the 1st Qual, if they win then they could possibly play a Southern League Premier team (Level 7), and then up to National League Premier (Level 5) in Qualifying Rounds 3 and 4. In the Rounds Proper, the Football League Divisions 1 and 2 join in (Levels (3/4), and at the 3rd Round Proper, The Premier League and Championship (Levels 1/2) are included.

So what we could have in TE is the first couple of rounds in the Cup being against teams of your own Level, and then from the Quarter-Final onwards, you could mix in teams from +/- 1 or 2 Levels to make the later rounds more interesting.