What would be the opposite of multicollinearity? Suppose two variables are perfectly uncorrelated (in a multiple regression with three parameters say), rather than perfect collinearity. What would this mean exactly? 
 A: One consequence of such an orthogonal or "balanced" design: The estimated coefficients of the two variables will equal those of the two corresponding simple linear regressions.
Check for instance the following example in R:  
# Generate two uncorrelated variables by PCA. The variables are shifted by two
#   to avoid side effects from being centered
pc <- princomp(iris[c("Sepal.Length", "Sepal.Width")], cor = TRUE)$scores + 2
zapsmall(cor(pc))

# The two selected principal components are really orthogonal/uncorrelated
       Comp.1 Comp.2
Comp.1      1      0
Comp.2      0      1

# Now, compare multiple regression with the two simple regressions
lm(iris$Petal.Length ~ pc)

# The multiple regression result
(Intercept)     pcComp.1     pcComp.2  
      7.903       -1.447       -0.625

# Now only the first guy...
lm(iris$Petal.Length ~ pc[, 1])

# ... has the same slope
(Intercept)      pc[, 1]  
      6.653       -1.447

# So does the second one
lm(iris$Petal.Length ~ pc[, 2])

(Intercept)      pc[, 2]  
      5.008       -0.625 

Thus, the ceteris paribus interpretation ("... holding the other variable fixed") makes perfect sense in such scenario. The higher the variables are correlated (e.g. age at diagnosis and time between diagnosis and study entry in a clinical trial), the stranger such interpretation usually is.
