Version:           3.4.1 (using KDE KDE 3.4.1)
Installed from:    Gentoo Packages
Compiler:          GCC 3.4.4 
OS:                Linux

Konqueror says that it accepts the following encodings:
x-gzip, x-deflate, gzip, deflate

However, if you try to use deflate with Konqueror it claims the page is corrupt. The code I use is:

std::string page_data = ...;
unsigned long bufferlen = page_data.length();
unsigned char* buffer = new unsigned char[bufferlen+1];
unsigned long out_bufferlen = long(bufferlen*1.1f) + 12L; // requirements of zlib::compress2
unsigned char* out_buffer = new unsigned char[out_bufferlen];
memset(out_buffer,0,out_bufferlen);
strcpy((char*)buffer,page_data.c_str());
compress2(out_buffer,&out_bufferlen,(const unsigned char*)buffer,bufferlen,1);
std::cout << "Content-Type: text/html" << std::endl;
std::cout << "Content-Encoding: deflate" << std::endl;
std::cout << "Content-Length: " << out_bufferlen << std::endl;
std::cout << std::endl;
std::cout.write((const char*)out_buffer,out_bufferlen);

This is from a cgi program in C++ using zlib for compression (include zlib.h and link with -lz).

This code works with Opera, Mozilla, Netscape, Firefox and Internet Explorer, so I think this problem is in Konqueror's support.