Best bet is to write WAV files with ulaw or alaw compression (the mFormatId of your AudioStreamBasicDescription would be kAudioFormatULaw or kAudioFormatALaw. Test to see which one gives you the smallest file sizes for your application.

Here s some code to set up an ExtAudioFile instance to write ulaw:

NSArray * docs = NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES);
NSString * docDir = [docs objectAtIndex:0]; 
NSURL * outFile = [NSURL fileURLWithPath:[docDir stringByAppendingPathComponent:@"OutFile.wav"]];
AudioStreamBasicDescription asbd;
bzero(&asbd, sizeof(asbd));
asbd.mSampleRate = 11025; // or whatever
asbd.mFramesPerPacket = 1;
asbd.mChannelsPerFrame = 1;
asbd.mFormatID = kAudioFormatULaw; //or kAudioFormatALaw
ExtAudioFileRef theFile;
err = ExtAudioFileCreateWithURL((CFURLRef)outFile,
                          kAudioFileWAVEType,
                          &asbd,
                          0,
                          kAudioFileFlags_EraseFile,
                          &theFile);

Hope that helps.

--- ADDED ---

Here are modifications to the SpeakHere sample code to get ulaw compression:

SpeakHereController.mm:116

recordFilePath = (CFStringRef)[NSTemporaryDirectory() stringByAppendingPathComponent: @"recordedFile.wav"];

SpeakHereController.mm:158

recorder->startRecord(CFSTR("recordedFile.wav"));

AQRecorder.mm:192

SetupAudioFormat(kAudioFormatULaw);

AQRecorder.mm:215

XThrowIfError(AudioFileCreateWithURL(url, kAudioFileWAVEType, &mRecordFormat, kAudioFileFlags_EraseFile,
                                      &mRecordFile), "AudioFileCreateWithURL failed");

Although a long time since the last post, I found the answer to the problem user196004 was having not being able to save to a folder OTHER than the temporary folder.

AudioFileCreateWithURL takes a CFURLRef as input. If the url is created using CFURLCreateWithString, and the destination folder has any spaces in it, the creation of the url will fail (null).

The solution is to escape the string.

CFStringRef fileNameEscaped = CFURLCreateStringByAddingPercentEscapes( NULL, fileName, NULL, NULL, kCFStringEncodingUTF8 );