TCA and Jessner Peel for Better Results?

This is a reasonable and graduated approach to the peeling process. A Jessner peel in and of itself does little. In combination and as a prep for the TCA peel, the two can provide a gentle and more agressive approach than the TCA byu itself.

A 20% TCA peelis a very minimal peel for facial skin improvement. I prefer 50% Glycolic acid peels with 10% glycolic home maintenance. Nevertheless, if you would like to stay with 20% TCA peels, adding Jessners solution would yield better results than the TCA alone.

Combination peels are more effective than single acid peels. Another choice which works better for some people is the "glycolic-TCA peel" which has been shown to be highly effective in several articles in the journal Dermatologic Surgery.

A TCA and Jessner's combination chemical peel, originally described by Monheit, is definitely stronger than a TCA peel alone. In fact, it's an order of magnitude higher, going down to the dermal layer of the skin rather than just the epidermis. It also requires such things as prophylactic antiviral medications to protect you against herpes simplex (cold sore) outbreaks over the face. This combination is considered a medium depth peel, and has much more downtime than a TCA light chemical peel. Expect peeling for 4-5 days and redness for 2 weeks, but good results with regard to sun damage, texture, and pigmentation. Being a more invasive procedure, it's also more expensive.
How good your results will be depends on what you're using it for... this is the key question. Are you trying to improve photodamage and skin texture? Then it's a great peel. Are you trying to improve fine lines and wrinkles? This peel will get you closer than TCA alone, but other modalities or a stronger strength TCA (but don't go higher than 35%) may be necessary.

A good option to get more results, without using a stronger acid is to layer more than one acid. This is a published procedure and is a common practice among dermatologists.