There's a Hole in My Bucket, Theory

From Hansen et al, 1981, page 6, column 3 we get the analogy of the leaky bucket: A bucket with a hole in it has water running into it at a constant rate and leaking out through the hole at the same rate, meaning that the level in the bucket remains the same. If the hole is made smaller, the level of the water in the bucket rises until the pressure is such that the flowrate of the water out through the new, smaller hole once again matches the flowrate of the water entering the bucket. The bucket represents the Earth's atmosphere, the incoming water is incoming solar radiation and the outgoing water is heat radiated back from the Earth into space. The hole represents the Greenhouse Effect (GHE) controlling the outgoing radiation. As the CO2 levels in the atmosphere increase, so the GHE increases and outgoing radiation decreases. This is represented by the hole getting smaller. More heat retained causes the temperature to rise, and this produces more outgoing radiation until the equilibrium is re-established, just as the water level in the bucket settled down to a new, higher level.
Now the problem with this analogy is the same holds true for a change in the amount of water entering the bucket, assuming the hole remains the same size. More water coming in means that the level rises, less means it falls, therefore an increase in solar energy reaching the Earth would cause a temperature rise, a decrease a fall. However, this is not borne out by observations. From that ever-useful site, Skeptical Science, we find this graph:

which quite clearly shows that the amount of incoming radiation from the sun has been reducing since about 1980. Up to that point, once you allow for a lag between increasing solar radiation and atmospheric temperature, there is a strong correlation between the two. After that there is none.
The only possible explanation is that the GHE only really kicked in around 1980, however a glance at CO2 levels over time, while it shows that the rate of increase of CO2 went up after 1960, does not show an increase that would account for almost zero affect up to 1980 and sufficient effect thereafter to cause warming despite a fall in the intensity of incoming solar radiation.
So either the rise in the water level in the bucket is due to more water coming in, which would be correct up to 1980, or it is because the hole is getting smaller, which would be correct from then on, but it can't be both.