Psoas (major and minor) is an important consideration, as is iliacus, together known as iliopsoas. Strength and flexibility are both important, to be sure. The one thing that many therapists miss in regards to back pain, unfortunately, is that the low back needs, above all, ENDURANCE (Type I muscle fiber), not strength per se (not Type II muscle fiber). That is, training power or strength (strength as in low rep, high weight training) to reduce low back pain will result in failure. Those who debate this point simply have no idea about LBP research or reality. Seated exercises are also a very bad idea, since sitting places MORE stress on the lower back than standing, and exercises like seated ab crunches or extensions, or even worse, seated rotations, actually cause MORE INJURIES than they were designed to prevent. These facts are often missed by well-meaning physical therapists, personal fitness trainers, and even chiropractic physicians, who ought to know better. Most medical doctors are usually not well educated in musculoskleletal medicine, either.

Muscles to pay attention to when experiencing LBP are:

multifidus and other erector spinae
quadratus lumborum
transverse abdominus
iliopsoas
rectus abdominus
abdominal obliques, internal and external
gluteals (maximus, medius, minimus)
hip rotators (piriformis, etc.)
hamstrings
hip abductors

These muscles need:

balance (i.e., symmetry), especially the lateral muscles such as quadratus lumborum and iliopsoas and lateral hip rotators such as piriformis

flexibility, especially erector spinae, iliopsoas, hamstrings and lateral hip rotators

stability (all muscle groups)

endurance (all muscle groups, especially core muscle groups)

Testing these parameters is the job of the chiropractor or physical therapist; it is likely that no other medical provider or therapist/trainer will have the knowledge to do those tests. The tests are simple for the DC or PT.

Training must be gradual, orderly, progressive and safe. For chronic LBP sufferers, it is unrealistic to think a few weeks will be enough to solve the problem. Chronic LBP sufferers will need MONTHS to begin to address their dysfunctin and approach a cure.

Advice to treaters of LBP: read Stuart McGill until you understand him cold.

I'll let you in on a secret: Most LBP sufferers, especially chronic sufferers, ALREADY have excellent muscle tone in their "low back muscles" (erector spinae). That's because they OVERUSE those muscles and strain them, leading to scar formation and chronic re-straining. Ever notice how people who don't exercise get a FLAT BUTT? My experience is that ALMOST ALL of my chronic non-discogenic low back pain patients have no butt. The good news is that there is now a surgical procedure to correct this problem. It's called an addanasstomy. Stumped? Don't worry, most M.D.'s are as well. Let me repeat: add an ass to me. Now you get it. Most LBP is the result of back overuse and weak gluteals. So, to be brief: get an ass.