Convey Complex Actions Off-Screen
If you don't see it, you don't have to animate it. Clever editing and sound FX can convey actions happening off-screen, reducing the total amount of character animation needed for a story.
For example, in the sixth episode of the melodramatic Revolutionary Girl Utena TV series, Nanami pleads to her brother Touga in a cafeteria to protect her from what she perceives to be assassination attempts on her life. Cut to a closeup of Touga casually remarking that Nanami has a hyperactive imagination. While still looking at this closeup of Touga, you hear a massive crash of dishes. Cut to a long shot revealing a held cel of a frantic Nanami on the lunch table, begging for his help, with dishes lying scattered everywhere. Clearly, she has jumped onto the table and scattered the dishes, but this complex action happened off-screen, conveyed solely by the sound effect of the crashing dishes and the held cel of the aftermath.
(In contrast, the far more expensive-per-minute Memories film features at least two shots of people knocking and scattering things everywhere while on-screen during the "Stink Bomb" segment).
Reduce the Number of Characters On-Screen
...that way more of the animator's attentions can be devoted to each character on the screen.
In 3D, this goes further -- fewer characters usually means faster system updates for LightWave (Messiah's incredible speed aside).
Reduce the Amount of Animation Involving Character Interaction
One character's tough enough. Hand-to-hand combat or even a dance between two characters is even tougher. You not only have to think for both characters, but the physics of their interactions with each other must also look convincing. (Notice that a number of the fights in Fatal Fury -- the Motion Picture involved energy blasts, instead of straightforward hand-to-hand combat like the incredible kickboxing match shown early in the film).
In 3D, this goes further -- physical interaction between two characters probably requires more complex character setups to make it easier for the animator.
Held cels involving character interaction seems easier to me. Allen Schezar's gentle hands resting on Hitomi's shoulders as he speaks to her in Escaflowne, for example.
It also seems easier to animate character interaction when the characters touch less of each other. For example, notice that in the scene where the angel swoops down to rescue the falling Hitomi in Escaflowne, only their hands interact (by grasping each other). After a shot of her shocked face, the next shot shows her waking up. You don't actually get to see the angel's other arm wrap around the rest of her in that scene (which is what I think he would have done to get a better grip, to better carry her to safety).
Intercut Complex Character Animation with Simpler Shots
In "Magnetic Rose," the first story of Memories, simple character animation shots (such as that of a talking, seated astronaut reading the display of the ship's computer) and simple non-character animation shots (such as that of an SOS alarm going off) are often intercut with complex character animation shots (such as that of another astronaut exploring a ghost ship). The simpler animation tides the viewer over inbetween complex shots. Along with the incredibly high quality of everything else (from story to design), the blend of the simple with the complex animations helps to stretch out the feeling of watching 100% complex animation. (In my opinion).
(It doesn't hurt to make sure everything else is top-flight. The viewer will subconsciously think: "100% of everything else looks expensive, so the animation must be 100% expensive all the time, too").
(If you don't believe that last paragraph, let me confess here and now that back in college, before I started doing animation for a living, I walked out of a 1996
Animania screening convinced that the highly entertaining Birdy the Mighty OAV series I had just seen looked better than Disney. Professionals will find this a laughable claim -- Birdy the Mighty clearly had a fraction of a Disney film's budget -- but to me the characters felt that real, and the fight scenes looked that cool).