I have a 2006 Liberty CRD with 4-wheel drive and a 2003 Honda Odyssey front-wheel drive van.

I have always shifted from Drive into 2nd or 1st gear on the fly while I was already in motion - especially when about to attack a particularly steep hill near my house. In a regular front-wheel van, this particular hill is pretty straining. In the Jeep, it's fine, but there is traffic behind and below, so I worry about making it up sometimes in certain road conditions. I've been told that is okay to shift on the fly, but the owner's manual does not specify if you can do that or if you have to be stopped to shift.

How are you supposed to shift into 2nd or 1st gear?

An automatic "should" take care of getting you into the proper gear (e.g. downshift) on its own. However, if you want to force, so to speak, the transmission into a lower gear then I see no reason why you could not shift on the fly EXCEPT you would need to be conscious of the speed and rpms involved. To state the obvious you don't want to attempt to shift from D to 1 at say 60mph.

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Sold to LOST member my 05 Ltd, GDE Stg II turbo + TCM tune, SunCoast TC w. Transgo kit, Steiger window regulators, Samcos, Fumoto valve, 2nd gen filter head with Lub. Spec. bleeder, Hayden clutch & 11 blade fan, inverted spare, P-1 battery, BF Goodrich Long Trail TAs, Etecno1 glow plugs, timing belt at 50K miles/8 yrs

Yeah, LOL. I just heard a guy on Car Talk say he shifted to 1st on the fly - trying to impress and old girl-friend. He obviously fried 1st gear! Duh! Some impression! He had no idea he couldn't do that. He had some misconception about if you did it a certain way it was fine.

As for shifting automatically - I just figure it is better on the transmission and engine if I already prepare for the steep incline which often has loose gravel. It's a city street, but I can't get up it in my little 4-cylinder car unless I have good speed and no one gets in my way! Most people can barely walk it. It is nearly impossible on bicycle - and dangerous when you stop. I stopped going that way in the little car, though, because it is a very, very old car with lots of rust and the danger of not making it is way too great. I rarely ever take my Odyssey that way, now, either, after replacing a transmission. I put it in Drive 1 or 2 before attempting it on the rare occasion I do go that way.

I figure the Jeep can make it, but I just get nervous if I hear the engine working too hard.

Must be really steep. Your CRD, like all diesels, has a massive amount of torque at lower rpms in contrast to a gasser. If it was me I'd just leave it in drive but, given the gravel, shift into 4-wheel full time (not part time) and drive up it that way. Otherwise shift into 4-wheel drive and at an appropriate speed shift into 1 or 2 then drive up it.

I suspect the CRD has enough torque to darn near drive up a vertical slope if only the tires had traction.

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Sold to LOST member my 05 Ltd, GDE Stg II turbo + TCM tune, SunCoast TC w. Transgo kit, Steiger window regulators, Samcos, Fumoto valve, 2nd gen filter head with Lub. Spec. bleeder, Hayden clutch & 11 blade fan, inverted spare, P-1 battery, BF Goodrich Long Trail TAs, Etecno1 glow plugs, timing belt at 50K miles/8 yrs

And if there is a danger to spin the wheels, use 4low and the wheels won't spin a bit

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2005 kj CRD, samco, suncoast tc, provent, Kennedy lift pump, GDE ECO full torque, 2nd gen filter head, 245/70/16 a/t tires, mopar light bar, fumoto oil valve, OEM Skid Plates, ARB Front bumper and HD OME, tru cool LPD47391 40k GVW tranny cooler (stock cooler delete), FF Dynamics e-fan and shroud, rocker arms replaced, HDS2 190F thermostat.