Starting from the 1986 districts...

Let's start from the 1986 district boundaries, as the City Charter calls for.
Since Downtown has added lots of housing over the last quarter century, we need to move lots of people out of District 4.  Likewise, a boom in student housing construction, including several new high-rises near Telegraph, requires us to move lots of folks out of District 7.  
Other than that, the hillside districts need to gain people, while the western districts are about the right size.  District 3 is more or less fine as it is, with the current population inside the 1986 boundaries within 1% of one eighth of the city. 

Here's a mathematically elegant plan that starts from the 1986 boundaries and equalizes the population in six moves. 

Move A: District 1 needs 639 more people.  Conveniently, District 2 has 525 too many.  The first move has District 1 cross south of University one block between San Pablo and Sacramento.  This brings in more folks within walking distance of North Berkeley BART, which is near the population center of District 1.

Move B: After giving 686 people to District 1, District 2 now is short 161.  These will come from District 4, which has plenty to spare.  Two blocks near Dwight and Sacramento are chosen to keep District 4 as compact as possible. 

Move C: The biggest move is 1,822 people from District 4 into 5 near Cedar and MLK.  Since the council member of District 4 lives right near the 4-5 border, this move needs to sidestep that block and go further south, instead of just taking District 4's northern blocks.  A side benefit is it preserves the downtown corridor of Shattuck Ave. within District 4.

Move D: District 6 is limited in where it can expand: two of its neighbors, Districts 5 and 8, have no people to spare.  Further expansion into District 7 requires crossing the UC campus.  Fortunately, District 4 still has more residents to spare. 

Move E: Well, after the last 3 moves District 4 is actually short a few hundred.  These will have to come from District 7.  The two blocks near Bancroft and Ellsworth, closest to Downtown Berkeley BART, are selected.

Move F: Finally, District 8 needs about 900 folks from 7 to balance the two out.  To preserve District 7's integrity as the Telegraph Ave and student housing district, this move comes out of 7's southeast corner.