We show that the properties of the electron beam and bright x rays produced by a laser wakefield accelerator can be predicted if the distance over which the laser self-focuses and compresses prior to self-injection is taken into account. A model based on oscillations of the beam inside a plasma bubble shows that performance is optimized when the plasma length is matched to the laser depletion length. With a 200 TW laser pulse, this results in an x-ray beam with a median photon energy of 20 keV,
>
6
×
10
8
 
 
photons
above 1 keV per shot, and a peak brightness of
3
×
10
22
 
 
photons
 
s
−
1
 
mra
d
−
2
 
mm
−
2

(
0.1
%
 
 
BW
)
−
1
.