Get Up & Move
Some of us don't feel like Gumby naturally, even if we actually have pretty good mobility. Often I see lifters feel stiff and uncomfortable in their workouts until they're nearly finished, at which point they observe they finally feel "warm". This should tell you that you need to change something - if you know you can get warm and feel loose eventually, it makes sense to figure out how to get that feeling at the beginning of your workouts instead of waiting until the end.
One effective way of doing this, which is less of a hassle and less of an energy drain than just warming up dramatically longer, is to get some physical activity in first thing in the morning. This can take a lot of forms, but the simplest would be running through a dynamic warm-up similar (or even identical) to what you do as part of your actual training warm-up.
This helps neurologically reset your body after it's been sedentary and in shortened positions all night, and makes it much easier to get warm and loose later for training. If you have time, precede this with a hot shower. If you have to train first thing in the morning, that hot shower will be even more helpful.