I don't know about you, but I learned long ago that when you are fishing to selective trout (dry, emerger/cripple or floating nymph), presentation is almost everything. The absolute perfect fly will almost always be refused by a selective trout if the fly is not perfectly presented to the fish within the fish's "feeding window". If you are fishing in moving water, a good presentation is all the more difficult due to the presence of multiple currents that can affect almost everything (fly line, leader, tippet and the fly. It is the drag that these currents create that is most often the reason your presentation is less than perfect and the trout refused your perfect fly. Selective trout all have an almost magical sense of "normal" or should I say "natural". If your fly moves unnaturally even the slightest bit once it is in that trout's "feeding window", there is a high probability your fly will be refused. Obviously, drag on your fly is a problem but there are several things you can do to reduce it.

1. You can change your position to create a better angle to the fish so that you are casting across fewer of these differing currents. This usually means positioning yourself more above or below the fish. Sometimes you can just slowly move closer to the fish but this carries a higher risk of spooking the fish. Do not assume that if you move more than 90 degrees below the fish that it cannot see you...it can. To become invisible to the fish, you need to be almost directly below the fish.

2. You can use longer, thinner and more supple leaders and tippets to help reduce drag on the fly.

3. You can understand and practice proper "mending" techniques and the "reach" cast.

4. You can use various "presentation" casts that put more slack line/leader on the water and this can give you a longer "natural" drift to the fish. Depending on your fishing situation, here are several of the presentation casts I have found to be of value. 

Reach Cast - The reach cast is very useful in many situations where you are casting across different currents and need to get a longer drag-free drift. You can also call it the "aerial mend cast"

Tuck Cast - The tuck cast is very useful when you want to get your nymph or streamer deeper into the water column faster and leave behind some leader and tippet so you get a longer "drift". This one is pretty simple.

Curve Cast - The curve cast bends either to the right or left of you and is a "hybrid" of the standard overhead cast. Curve casts are used  when casting the fly around objects on the surface or when you need to prevent the leader and fly line from "spooking" a fish as the fly passes over the fish.

Pile Cast - The pile cast is very useful when you are above a fish. It really a "presentation" type cast. With this cast you "pile" up the end of the leader and tippet to get a longer drag free drift over your target.

Slack line or Serpentine Cast- This is primarily a dry fly cast. It is also called a "wiggle" cast. Like several other cast, it puts slack line on the water and this gives you a longer drag free drift over a rising fish. It is very good when you have variable currents between you and the fish.This is a pretty easy cast to learn.

I have mentioned a trout's "feeding window" several times above. This is a cone of "acute" visibility within which a trout looks for food. This cone is approximately 97 degrees. If you are a fly fishing nurd...I guess that includes me, there is a series of long and very interesting and educational videos that all truly serious trout fishers should watch. There is a lot of valuable information about what a trout sees as well as interesting facts about what the fly fisher sees...or thinks they see. Here are the links to these videos. I recommend watching them in order...make a big bowl of popcorn first.

These videos were done by Wendell "Ozzie" Ozefovich

The Underwater World of Trout Part One | Discovery

Underwater World of Trout Part Two | Feeding Lies

Underwater World of Trout Part Three | Trout Vision