This problem is most common in cabinets incorporating only a single speaker, often the situation with combo amps and the add on cabinets made for them. There is no substitute for a quality driver. A name brand speaker with a generous wattage ratting is a must. Most guitar speakers have a paper surround that gives a nice cone breakup distortion when played at high levels but those wishing the cleanest sound and the most honest reproduction of what's coming out of the amp can chose a model with a cloth surround. Eights and tens have a tight crisp tone but lack bass.
Fifteens supply the most bass but can be mushy sounding.
Although all sizes have their purpose twelves offer the best of both worlds and are preferred by most players. If regularly playing at higher sound levels it's a good idea to use cabinets with paired rather than single drivers. While cabinet and speaker design are important factors the other variable of equal import is also the most overlooked. All other factors being equal placement can make or break the sound. A rear wall or corner placement can really beef up the tone especially with an open back where the sound radiated from the rear reflects around to the front and reinforces the forward radiated sounds.