The more excess capacity the unit has the worse the humidity removal becomes.

The excess capacity means the unit has shorter run times, limiting humidity control.

It gets worse if the temperatures are below the design point for the system.

How long does the unit run? And how often does it come on?

It is possible that the new attic insulation meant that you need even less cooling so you are even more oversized than you think. That could lead to humidity problems.

But 58% sounds shocking. 47% is what I get in NC if it is cooler outside and pretty humid. Could there be a plugged condensate line? Do you run the fan all the time? What was the size of your last unit?

Did the previous 3 ton unit ever have trouble keeping the home cool/comfortable?

None. It was find until the condenser started going.

'design point' is (more or less) the temperature point at which the system is designed to operate at greatest load. That is, lets say maintain 72F when it is 110F outside. This along with what is known about the insulation, sun load on the house, windows, shading, etc, will determine how large a unit is required.

If your 3 ton unit had no issue keeping the house conditioned and you added more insulation, you definitely don't need anything more than a 3 ton unit. The 4 ton unit you have now provides too much cooling and is causing the unit to short cycle. The unit needs to run a while to dehumidify the space. I'd see what you can do to reduce your unit to a 3 ton unit at least.

The company does not want to reduce the unit size, but wants to customize a program through Lennox to blow less cool air over a longer period of time to dehumidify. They said this will decrease my efficiency, and increased efficiency was why I got the unit in the first place. Should I get a disinterested third party to repeat the manual J?

I don't really think you need a manual J. 3 tons worked fine and now you are oversized - case closed.

But if you need leverage over your HVAC company, it might be the way to go. I feel for you - you need a 3 ton - I just hope you can convince the HVAC company to do it. I had a HVAC company install a 4 ton as a mistake so it wasn't hard to get them to replace it with a 3 ton.

Leverage comes from BBB, state licensing bureaus, and manufacturer authorized installer programs (I'm not sure how helpful that one is...).

What exactly does the manual J numbers say? sensible,latant, design temps in and out?
you basicly have an over sized unit and if slowing down the air speed didn t help the nothing much to do but down size.
air hander in attic? check for major air leaks.

That's what I say (oversized unit). They don't seem to be willing to do that. And, I don't have a copy of the manual J. That's just what I was told (3.5 tons). One serviceman from the company told me that there is cold air blowing in the attic. Oy! Last night's sleep was horrible. Even at 72 degrees, it's warm in here with 45% humidity. Remember, I live in Phoenix. With the other system,I was FREEZING at 77!

I have owned this Maytag 23 SEER IQ Drive equipment from Nordyne (both a 3 ton & a 2 ton unit)since April 2009. I replaced two old, inefficient systems in their entirety. I paid top dollar for this high efficiency equipment and boy was I taken! Lots of service calls (more in 1 year than in the 11 years I owned the older units); high humidity inside the house (a new problem that started with the install of this equipment); noisy fans that wake me up when the units shut down at night; no improvement in energy efficiency at all (I have to keep the house 4 degrees cooler than with the old equipment to keep from sweating, due to the high humidity); equipment is sensitive to power fluctuations (computer brain flips out every time there is a switching transient from the power company and must be reset); and the list just goes on and on. I would NOT recommend purchasing this product. A Trane 2 Stage system would likely be a much better investment (note: I have never owned Trane equipment and I don't know anyone who works for Trane - it just happens to be the alternative I investigated before deciding to buy the IQ Drive.)

A new twist: I've turned the temperature down on the unit, and the humidity is rising. Shouldn't more time/cool air over the coil be extracting humidity? Was at 45%, now at 48%. I'm so tired of this!!!! Any thoughts?

I've had similar problems since installing a Trane XL16 near end of June. MANY service calls. Changed return size, changed supply duct from flex to hard, fan speed, and so on. My humidity got as high as 74. I'm now about $10K out of pocket exploring what is the problem, engineers and all kinds of expenses involved with moisture mitigation-even dug up my yard and installed a water meter because AC co. said I 'must have a water leak'(I'm on a well so no meter before). No leak. It has even been suggested that the lightning strike which caused me to need a new HVAC caused the ground to shift and an underground spring to come to surface. I now have mold, been advised to leave my home and I have an attorney involved. Do whatever it takes to get the unit properly sized or correct whatever the problem is NOW-before your problems get much worse. I wish I'd turned off the unit and used temporary air until I found the problem, but I too kept hearing 'this will fix it' over and over. Sorry I have no concrete suggestions to fix your problem. Is there anyone out there who might help me?

its gotta be fan speed. If the A/C is working the indoor coil will be getting cold. If the fanspeed is high the indoor coil doesn't get as cold (but moves more volume of air). If the fan speed is set appropriately then the indoor coil gets cold enough and condensation builds up on it (dehumidifying).

Does this AC unit still cool good? Does it blow nice cold air?

Does it pull out any water at all? Maybe the condensate drain is clogged.

"its gotta be fan speed."

Oversize units do not run long enough to control humidity well.

Except in commercial work humidity sensors are rarely used to control AC.
If the system is correctly sized it will have long enough cycles to remove humidity.

If it is excessively large it drops the air temperature so quickly little moisture is removed and cool and clammy is the result.
The thermostat ONLY measures air temperature.

I thought the users new system was the same size as the old system which worked fine. If the unit short-cycles you could replace with a thermostat that has a control for cycle time.

I agree, oversized is not right. But it sounds like he isn't if I read the thread correctly.