What kind of light? 6400 lumens is not enough at several feet away. H.I.D. usually produces much more than 6400 lumens. Also what spectrum? You need a spectrum around 6500 kelvin to keep plants short and stocky. Either metal Halide or flourescent. How much area are you trying to light? I don't consider 6400 lumens at several feet to be "plenty of light." Keep the light source as close as possible without causing leaf burn. Within inches if possible.
Good Luck,
Ken

The 6400 lumens are from a 4-tube fluorescent fixture (plant and aquarium bulbs) suspended about 2 feet above the plants (1 foot from the higher ones). There are four (soon to be six) pots, all directly under the fixture. There is also natural light in the room during daylight hours, althought not much direct sunlight on the plants. I run the lights about 15 hours a day...maybe I should run them longer? Thanks for your help.

Do you have any kind of fan for these plants? A gentle breeze will help toughen up those stems.

6400 Lumens? The problem is almost certainly LOW LIGHT level.

I have a T5 fixture above a coco garden about 18" from the soil level, about 4" from the tops of the plants and they do beautifully.

Lower your lights and see how they do! For vegetative growth 24 hour lighting is not unusual, although 18/6 is more common here where we are.