This paper reports a high-resolution experimental study of the
3
3
Π
g
and
4
3
Σ
+
g
electronic states of the
85
Rb
2
dimer. In the experiment, rovibrational levels of the two electronic states were probed using the perturbation facilitated optical-optical double resonance technique by exciting
85
Rb
2
molecules from thermally populated levels of the ground
X
1
Σ
+
g
state through intermediate levels of the mixed
A
1
Σ
+
u
∼
b
3
Π
u
electronic states. The resonances of the probe laser were observed by detecting the laser induced fluorescence from the target states to the
a
3
Σ
+
u
triplet ground state. In addition, to confirm the triplet character as well as the vibrational quantum number assignment of the states, for selected resonances the fluorescence to the
a
3
Σ
+
u
state was resolved and bound-free spectra were recorded. From the observed term values for each state potential-energy curves were constructed using the Rydberg-Klein-Rees method.