Yeah, I pretty much agree with Roger. There are a few cases that grounds are not good for natural conditions: On a rock face, at altitude, or, in the stream. (Even in the stream doesn’t do any real damage, but it can influence local bacteria. Here in the ADK’s, with all the natural tannin in the water, even that can be ignored, but it creates an unsightly mess.)
In the woods, it is easy to simply walk 20-30yd from a camp site and give the grounds a good toss, effectively scattering them around on the forest duff. Basically, once brewed, they are simply a woody product subject to natural decay. Just do NOT leave grounds in piles. They are effectively sterilized and it can take a while for any decay process to utilize them.
I gave up on that stuff a while ago. Both GSI types were fairly messy to dear with. After the third spill, I just tossed the stand up drip filter when I got home. The other “collapsible” one didn’t work as well. Anyway, instant requires like a spoon and a half for a decently strong cup of coffee. The drip brewer always required three spoonfulls of finely ground coffee. So, the weight was a factor. Usually in the morning, I am busy packing. I get the stove going to boil the first cup, and pack my sleeping bag. I then roll up my pad and go back to mix up my mud, and start the full pot. As the cup cools, I change my cloths and finish packing all my dry gear, often delaying the final compression step while I have my jacket on. As I finish my first cup, I usually have my shoes changed and watch the critters for a few minutes. Then I turn off the stove and fix my second cup, and put the remainder under my hat. As my second cup cools, I usually UV one water bottle for hiking, and, dump in coffee and cocoa in the second. Then I pour in about a cup into that bottle and mix it. Then I take the tarp down and roll it up (if it isn’t raining.) Then I drink my second cup and fix my third cup, adding any remainder to the coffee bottle, reserving just enough to rinse stuff out/brush my teeth. I just sit and enjoy the surroundings as I finish my coffee. I do my morning clean-up chores then. I pack up all the odds and ends (stakes, tooth brush, paste, food bag, top off my coffee bottle, etc) and strip off my jacket, and compress my jacket, sleeping bag, long johns & socks and start packing my pack. Everything is pretty much ready to drop in. Compression sack, food bag, ditty bag (stove in the ditty bag,) spoon, stakes, tarp gets rolled into my pot, Pad slips onto my cup, sweater goes on top and I close it up. Drop my water bottles in one side, and fuel, windscreen, saw in the other. I sling it up and fasten it down, grabbing my staff, ready to hike. I take two or three steps away and stop to survey the campsite, insuring I didn’t forget anything. Instant coffee just makes it all go much easier than fiddling around trying to make 5 cups of coffee in the morning any other way. At 1000 on the trail, it is nice to have a still warm drink, unless it is cold out. Iced mocha is good anyway.


