mod_deflate is available in lighttpd 1.4.42 and later. mod_deflate differs from mod_compress in that mod_deflate can compress any output from lighttpd static or dynamic. mod_deflate does not support caching compressed output like mod_compress.

Module options:

deflate.mimetypes = ("text/html", "text/plain", "text/css", "text/javascript", "text/xml")
#deflate.mimetypes = ("text/")       # prefix matches all text/* Content-Type responses
deflate.allowed-encodings = ( "bzip2", "gzip", "deflate" )
deflate.max-compress-size = 131072   # measured in kilobytes, so 131072 indicates 128 MB
deflate.min-compress-size = 256      # measured in bytes
deflate.compression-level = 9
#deflate.output-buffer-size = 8192 = 2048
#deflate.max-loadavg = "3.50" 

max-compress-size is the largest response size that will be compressed.
min-compress-size is the smallest response size that will be compressed.

output-buffer-size is a per connection buffer for compressed output, it can
help decrease the response size (fewer chunks to encode). If it is set to
zero, a shared buffer will be used.

work-block-size is the number of kilobytes to compress at one time, it allows
the webserver to do other work (network I/O) in between compression.

max-loadavg is max system loadavg before bypassing compression (since 1.4.43)

Known Limitation

mod_deflate currently does not stream compressed content in chunks. This affects very large dynamic responses, or dynamic responses sent in chunks with large time lapses between chunks.

(obsolete) patches to add mod_deflate to versions prior to lighttpd 1.4.42 (YMMV)