Publicly linkable resources without an integer id

For those of us who are writing Python web applications with RDBMS storage it is very tempting to create urls like http://hackingthought.com/foo/72 where the '72' represents an id to a record in the a table. This has never felt right for the basic security risk of I could easy guess the other records which I may not want publicly exposed. Example 73 or 74. For many reasons this is undesirable. In the case of a blog this is an acceptable behavior because we may not be concerned with the resources that are on the other side. In the case of video site like youtube I may not want just anyone downloading the entire collection of video content!
This is pretty easy to resolve by using Pythons built in uuid module. For a while I thought this was acceptable but then I started to think the urls that it would generate would be rather long. Example: hackingthought.com/foo/181067910632484385564896804811492956458! To me this is a bit excessive to use the integer uuid generates. To make my life a lot easier there is a built in representation of the uuid which is hex. hackingthought.com/foo/8838693e35534e86b442f9d8b8d6192a. Better but only saved 7 characters.
Even though 32 characters is not that painful it is still a bit long for my taste. hex is not ideal, base64 would use a lot more characters and reduce the size. This would produce: hackingthought.com/foo/iDhpPjVTToa0QvnYuNYZKg (after subtracting ==\n).
At this point I have gotten it down to 22 characters vs 32 hex or 39 integer. 43% Reduction!
The code:

import uuid
from base64 import b64encode
import timeit
k = uuid.uuid4()
# Unique id as an int
print('char length: %s type:int value: %s'
 % (len(str(k.int)), k.int))
# Unique id as an hex
print('char length: %s type:hex value: %s'
 % (len(str(k.hex)), k.hex))
# Unique as base 64
# Notice it replaces the + and / for chars that can work in a url
b64k = b64encode(k.bytes, '#$')
# Subtract formatting chars
b64k = b64k.replace('=', '').strip()
print('char length: %s type:hex value: %s'
 % (len(str(b64k)), b64k))

Performance? Well my laptop can generate 100K in about 6 seconds using uuid1 or uuid4 so I don't think that it is a bottleneck.
I wonder if it could be even shorter. I would love to know how to make them shorter without loosing any ease of use of built in python modules or writing of algorithms. Please drop me a line of you find another a better way to do this.