io.BufferedReader peek function returning all the text in the buffer

I am using Python 3.4.1 on Windows 8.

I would like to read a file with a buffered interface that allows me to peek a certain number of bytes ahead as well reading bytes. io.BufferedReader seems like the right choice.

Unfortunately, io.BufferReader.peek seems useless because it appears to just return all the bytes stored in the buffer, rather than the number requested. In fact, this is allowed by the documentation of this function (emphasis mine):

peek([size]) Return bytes from the stream without advancing the
position. At most one single read on the raw stream is done to satisfy
the call. The number of bytes returned may be less or more than
requested.

To demonstrate what I consider useless behaviour, I have the following test file called Test1.txt:

first line
second line
third line

I create the io.BufferedReader object like this in IDLE:

>>> stream = io.BufferedReader(io.FileIO('Test1.txt'))

and then ask for two bytes,

>>> stream.peek(2)
b'first linernsecond linernthird line'

Eh? That’s just all the text in the default buffer size (which is 8192 bytes on my system). If I change this default, I can confirm that peek() is just returning the contents of the buffer,

>>> stream2 = io.BufferedReader(io.FileIO('Test1.txt'), buffer_size=2)
>>> stream2.peek(17)
b'fi'
>>> stream2.peek(17)
b'fi'
>>> stream2.read(2)
b'fi'
>>> stream2.peek(17)
b'rs'

To be clear, the following is the output I expect to see:

>>> stream = io.BufferedReader(io.FileIO('Test1.txt'))
>>> stream.peek(2)
b'fi'
>>> stream.read(1)
b'f'
>>> stream.peek(2)
b'ir'

That is, a typical buffered stream.

What am I doing wrong in constructing this BufferedReader? How can I observe the behaviour I expect to see in Python 3.4.1?