I was reading about the fall of the Berlin wall, and German reunification, and in this wikipedia article about the 1991 Treaty on the Final Settlement with Respect to Germany ("Two Plus Four Treaty") it mentions that a united Germany wasn't fully soverign until then:
In the treaty the Four Powers renounced all rights they held in Germany, allowing a united Germany to become fully sovereign the following year.
and
This meant that in some respects (largely, but not only, technical), Germany did not have full national sovereignty.
And the article on German reunification states:
Other negotiations between the GDR and FRG and the four occupying powers produced the so-called "Two Plus Four Treaty" (Treaty on the Final Settlement with Respect to Germany) granting full sovereignty to a unified German state, whose two parts had previously still been bound by a number of limitations stemming from their post-World War II status as occupied regions
In what ways West & East Germany not fully independent?
The article itself alludes to the answer to your question.
The treaty allows Germany to make and belong to alliances, without any foreign influence in its politics. All Soviet forces were to leave Germany by the end of 1994. Before the Soviets withdrew, Germany would only deploy territorial defense units not integrated into the alliance structures German forces in the rest of Germany were assigned to areas where Soviet troops were stationed. After the Soviets withdrew, the Germans could freely deploy troops in those areas, with the exception of nuclear weapons. For the duration of the Soviet presence, Allied troops would remain stationed in Berlin upon Germany's request.
Basically the treaty removed the last vestiges of Allied (and Soviet) occupation of Germany. Up until that point, Germany was in some ways under the domination of foreign powers. For example, the Allied Powers retained a right to station troops in Berlin (and I believe the rest of the country).
What this treaty did was permit Germany to reunify (despite the initial opposition of Margaret Thatcher and the trepidation of Francois Mitterand) and renounced any say the Allies or Soviets had on Germany's affairs - therefore restoring full sovereignty.
Germany still allows allied troops within their borders as per their membership in NATO, but this is an entirely separate agreement and they could conceivably demand a withdrawal of all foreign forces from German soil if they wished.
I've tracked down a pdf of [The Convention on the Settlement of Matters Arising out of the War and the Occupation](http://treaties.fco.gov.uk/docs/fullnames/pdf/1959/TS0013 (1959) CMND-656 1952 26 MAY,BONN%3BCONVENTION ON SETTLEMENT OF MATTERS ARISING OUT OF WAR&THE OCCUPATION BETWEEN NI,FRANCE,USA&FEDERAL REPUBLIC OF GERMANY_1.pdf), which is as far as I can tell the relevant treaty that largely established the post-war-till-1991 relationship. And article 1 is the most relevant article.
I don't know much more, but as you can read what it seems to came down to is that Germany was in principle given full self-control in 1951, but for a range of issues it needed permission of the Three Powers in order to act. These seem to include: making changes to laws enacted by the occupiers, rights regarding Berlin, and issues of unification or territorial changes.