I've never had this problem before. My chain doesn't want to shift onto my third-position freewheel cog. It prefers to stop on the one before, or go on to the one after. If I finesse it just right, though, it WILL go onto the third cog, and works perfectly once there.
Other possibly significant details: Suntour VGT Luxe in back, Suntour SL (high normal) in front, downtube Power Ratchet shifters (friction, it goes without saying); 6-speed Suntour Perfect freewheel with 14, 16, 19, 22, 26, and 34 cogs (the 22 is the problem cog). Chainrings are 46-34, making it a slightly odd wide-range double setup with a double shift at the crossover. It gives me 8 unique ratios that are pretty evenly distributed, though weighted toward the low end--very nice for my needs. The 34 cog is my addition--it originally came with a 30-tooth low.
Any suggestions? I can't think of an adjustment that would touch this problem, and can't see any differential wear on the cog teeth or other obvious problems.

Clean or replace the shift cable. It happens a lot.

Cables and housings are new and correctly installed.

Jon, maybe the 22 tooth cog has a "warp" in it? Did you try swapping it out? If you need another 22 tooth Perfect cog I could drop one in the mail ASAP.

I had this happen once. The spacer was out out alignment, and was too high to let the chain drop onto the cogs. Worth checking.

Did you have the same exact problem before you replaced the cables?

I had a brand new inner cable get kinked before I put in on the bike,
it would stick sometimes even when correctly installed.

Did you have this problem before you changed the big cog?

It's a new-from-a-bare-frame-up build so it's the first time the parts have worked together. But it's done this from the beginning. I doubt that it's the cable, since with downtube shifters it's just a straight cable run with one nine-inch piece of housing right at the RD--not a whole lot of room for things to go wrong. But I will look with your suggestion in mind.

Thanks for the kind offer, Bob--that could be it, I suppose. I do have another 22-tooth cog here, so if I can't think of anything else, maybe I'll throw it on and try it.

Interesting--can you explain what you mean by "out of alignment," though? Not sure what to look for. My understanding has always been that the spacers and cogs just get stacked up and tightened in place. I can see how things could be too loose, maybe, but not misaligned, assuming that the parts went together in the right order. But I don't have a lot of experience reconfiguring freewheel cogs--maybe I'm overlooking something.

I have the same thing. SunTour 6 speed freewheel. The chain just doesnt want to drop in to one of the middle cogs. I have to fiddle with the lever and hit it just right. I can't figure it out and just put up with it, though at times it's frustrating. Sorry i can't help.

One spacer wasn't centered properly, and ran high on one side, preventing the chain from fully engaging.

If I understand correctly this is is a new old build up with 6 speed setup using a Suntour perfect pretty wide range. Try adding a single spacer to the drive side of the axel.

I think the key hint to the mystery is the cog switch-out. Some spacers are position dependent for width and shape as mentioned above. Every once in a while when taking apart a factory built freewheel paper thin steel spacers were found in between a cog here and there.

Clean freewheel.
Check for abnormal wear. (chain hitting top of spacer for example)
Check dimensions between cogs carefully.
Probable reassembly after some corrections.

I will give that a try, though I don't THINK the cog change had anything to do with it. I did take the bike for one ride before the cog change--which confirmed to me that a a 34-30 low wasn't going to be low enough for me--and I think it had the shifting problem even then. But since it was just that one ride and I probably only ran through the gears a couple of times, I can't say for sure. But it's worth a look.

Shimano makes a 6 speed freewheel with 14-16-18-21-24-34 cogs. IRD makes a 14-16-19-24-28-34. I'll bet an HG freewheel will do the trick.

Are they traditional wound housings (i.e., brake cable housings)? If so, get some Jagwire or Shimano SIS cable housing. I've found it makes a significant difference even for that little loop of housing back by the derailleur.

hmmm, i'm having the same issue with a Suntour VGT Luxe and an 8-speed Shimano freewheel. Running friction with Simplex retrofrictions and a Campy NR front derailleur. I can't get the rear derailleur to shift into the lowest and highest cogs on the cassette. tried everything, messed with the limit screws and changed the chain length around. I even tried two different Suntour VGT Luxe RD's, in case one had a weak spring. No dice.

In my experience Simplex retrofrictions didn't have the pull to to suit me with a 7sp freewheel, so I'd imagine an 8 sp cluster would be even worse. They were designed for 5 and maybe 6 speed freewheels.

Yup, they're new lined Jagwire casings--spiral-wound, as you say.
By the way, thanks for the haiku, which I find that I repeat it every time I go through a stop sign when there's no one around--which in my part of Vermont is most of the time.

ahhhh HA! I was guessing that it might be an issue with the levers, but hoping it wasn't (cause they are pretty awesome otherwise).

The giveaway for me is that it's a Suntour freewheel.The problem sounds to me exactly like the shy cog was put on backwards.I have come across this before, and with the exact same symptoms.Suntour cogs cannot be reversed without affecting the shifting, and it's even worse where a correctly-placed cog sits adjacent to a reversed cog.Look at the teeth, the differences on the two sides are deliberate and obvious.Shimano freewheel cogs of the Uniglide era cannot be assembled backwards. Shimano made sure of that!


EDIT: Note that the software deleted all of my sentence spaces and paragraph breaks. I'll mostly just use other sites until this gets fixed.

Odd that the problem doesn't occur when adding text using the EDIT function. Weird.

And if that's not weird enough, it now takes several, slow BACK commands just to get back to the Vintage section. Truly awful site performance.

Maybe your chain tension is too loose? Take a link or 2 out and the derailleur action may improve. Although I'd expect sloppy shifting at the bottom, not the middle.

If they are spiral (helix) wound, like brake cable housings, those aren't the right ones to use for shifters. If they have the longitudinal lay, with hardly any twist in the wires, you have the right ones.

I'm old school in that respect--spiral casing is what was available when this bike was new, so that's what I use. The shifter-type cable is really only useful and necessary with indexed shifting. I doubt that the compression in the 9-inch piece of cable right at the derailleur amounts to anything--I don't notice it in my friction-shifting bikes set up with bar ends, which have much, much more housing.

Aha! That sounds very plausible! I'll have a look.