You may keep them unless they are spotted from mites or leaf spot diseases. If your Cordyline is growing at an indistinguishable rate it will take longer for the plant to suck all the nutrients out of the browned leaves before dropping them naturally. Probably by now ( 9 months after your post) you can trim them off if they are the lower older leaves. Just know if you change anything about their culture they might bounce back to a deep maroon/brown green if they are lower leaves. A shocked cordyline will neglect to nurish 2/3 of lower leaves turning them an unattractive color but possibly without dropping them. If they are papery like papyrus then they are long dead and removing them is fine. Heck removing lower cordy leaves is always fine I'd just add a bit of nutrient solution to the next water bath and give them brighter shade for a few days. Remember low humidity will brown leaf edges working its way into the center. None of this applies if they are new leaves. I hope to see an update on how the color is now. I'm suspicious that the first post is actually 'kiwi' or 'pete's rainbow". Let me know if I didn't make sense or miscommunicated. My miss Andrea needs a humidifier and to be cool but my red sister doesn't and likes warmth. Hope that helps. I'm z7a in Nashville and all my Cordylines are indoor specimens that enjoy co-potting with tropical epiphytic vines for humidity and awkward small talk.

im not sure your presumption is correct ... why would two shoots from the same root mass ... interfere with each other ... so what if one is taller than the other... face the shorter one towards the sun.. and let it block the back one until it catches up ... i suppose the place to start .. wouldl be to baqre root it.. and SEE if it can even be divided ... if not.. repot.. and put in shade until the roots start pumping... if you can get root with each piece... divide it.. and dont look back .. or cut one piece off.. and root it... and leave the other with the roots ... https://duckduckgo.com/?q=cordyline+propagation&t=ffcm&iar=videos&iax=videos&ia=videos and figure out how to store it in winter ... so many options.. so little time .... ken

Not enough information to diagnose what afflicts the plant. How long have you had the plant? On average, how long between waterings? When you water, are you making sure the entire soil mass is soaked? Have you fertilized it? If yes, describe what you used and how you went about it. Flushing the soil when you water and allowing the medium to dry down to nearly dry will fix the mineral deposits on the soil's surface - no need to repot. It's best to use a 'tell' to 'tell you when it's time to water. Proper moisture management is an essential part of keeping your plants at a high level of vitality. Using a 'tell' Over-watering saps vitality and is one of the most common plant assassins, so learning to avoid it is worth the small effort. Plants make and store their own energy source – photosynthate - (sugar/glucose). Functioning roots need energy to drive their metabolic processes, and in order to get it, they use oxygen to burn (oxidize) their food. From this, we can see that terrestrial plants need plenty of air (oxygen) in the soil to drive root function. Many off-the-shelf soils hold too much water and not enough air to support the kind of root health most growers would like to see; and, a healthy root system is a prerequisite to a healthy plant. Watering in small sips leads to avoid over-watering leads to a residual build-up of dissolved solids (salts) in the soil from tapwater and fertilizer solutions, which limits a plant's ability to absorb water – so watering in sips simply moves us to the other horn of a dilemma. It creates another problem that requires resolution. Better, would be to simply adopt a soil that drains well enough to allow watering to beyond the saturation point, so we're flushing the soil of accumulating dissolved solids whenever we water; this, w/o the plant being forced to pay a tax in the form of reduced vitality, due to prolong periods of soil saturation. Sometimes, though, that's not a course we can immediately steer, which makes controlling how often we water a very important factor. In many cases, we can judge whether or not a planting needs watering by hefting the pot. This is especially true if the pot is made from light material, like plastic, but doesn't work (as) well when the pot is made from heavier material, like clay, or when the size/weight of the pot precludes grabbing it with one hand to judge its weight and gauge the need for water. Fingers stuck an inch or two into the soil work ok for shallow pots, but not for deep pots. Deep pots might have 3 or more inches of soil that feels totally dry, while the lower several inches of the soil is 100% saturated. Obviously, the lack of oxygen in the root zone situation can wreak havoc with root health and cause the loss of a very notable measure of your plant's potential. Inexpensive watering meters don't even measure moisture levels, they measure electrical conductivity. Clean the tip and insert it into a cup of distilled water and witness the fact it reads 'DRY'. One of the most reliable methods of checking a planting's need for water is using a 'tell'. You can use a bamboo skewer in a pinch, but a wooden dowel rod of about 5/16” (75-85mm) would work better. They usually come 48” (120cm) long and can usually be cut in half and serve as a pair. Sharpen all 4 ends in a pencil sharpener and slightly blunt the tip so it's about the diameter of the head on a straight pin. Push the wooden tell deep into the soil. Don't worry, it won't harm the root system. If the plant is quite root-bound, you might need to try several places until you find one where you can push it all the way to the pot's bottom. Leave it a few seconds, then withdraw it and inspect the tip for moisture. For most plantings, withhold water until the tell comes out dry or nearly so. If you see signs of wilting, adjust the interval between waterings so drought stress isn't a recurring issue. Al

Check for spider mites as this plant is a spider mite magnet. Cut off damaged leaves to pretty it up some. It loves the outdoor summer climate too. Unfortunately they are not winter hardy in the Atlanta area.