diff --git a/src/ocrmypdf/__main__.py b/src/ocrmypdf/__main__.py
index c154e888..3e69effd 100755
--- a/src/ocrmypdf/__main__.py
+++ b/src/ocrmypdf/__main__.py
@@ -294,6 +294,12 @@ optimizing.add_argument(
           "Values have same meaning as with --jpeg-quality"
     )
 )
+optimizing.add_argument(
+    '--jbig2-lossy', action='store_true',
+    help=("Enable JBIG2 lossy mode (better compression, not suitable for some "
+          "use cases - see documentation)."
+    )
+)
 optimizing.add_argument(
     '--jbig2-page-group-size', type=numeric(int, 1, 10000), default=0,
     metavar='N',
@@ -517,10 +523,26 @@ def check_options_optimizing(options, log):
         _optional_program_required(
             'pngquant', pngquant.version, '2.0.1', '--optimize {2,3}'
         )
+
+    if options.jbig2_lossy:
+        _optional_program_required(
+            'jbig2', jbig2enc.version, '0.28', '--jbig2-lossy'
+        )
+    elif options.optimize >= 2:
+        # Although we use JBIG2 for optimize=1, don't nag about it unless the
+        # user is asking for more optimization
         _optional_program_recommended(
             'jbig2', jbig2enc.version, '0.28', '--optimize {2,3}'
         )
 
+    if options.optimize == 0 and any([
+            options.jbig2_lossy, options.png_quality, options.jpeg_quality
+            ]):
+        log.warning(
+            "The arguments --jbig2-lossy, --png-quality, and --jpeg-quality "
+            "will be ignored because --optimize=0."
+        )
+
 
 def check_options_advanced(options, log):
     if options.tesseract_oem and not tesseract.v4():
diff --git a/src/ocrmypdf/optimize.py b/src/ocrmypdf/optimize.py
index cb940dc3..862bac6a 100644
--- a/src/ocrmypdf/optimize.py
+++ b/src/ocrmypdf/optimize.py
@@ -30,7 +30,6 @@ from . import leptonica
 from .helpers import re_symlink, fspath
 from .exec import pngquant, jbig2enc
 
-DEFAULT_PAGE_GROUP_SIZE = 1
 DEFAULT_JPEG_QUALITY = 75
 DEFAULT_PNG_QUALITY = 70
 
@@ -363,7 +362,7 @@ def optimize(
                 DEFAULT_PNG_QUALITY if options.optimize < 3 else 30
     if options.jbig2_page_group_size == 0:
         options.jbig2_page_group_size = \
-                DEFAULT_PAGE_GROUP_SIZE if options.optimize < 3 else 10
+                10 if options.jbig2_lossy else 1
 
     pike = pikepdf.Pdf.open(input_file)
 
@@ -401,12 +400,14 @@ def main(infile, outfile, level, jobs=1):
     class OptimizeOptions:
         """Emulate ocrmypdf's options"""
 
-        def __init__(self, jobs, optimize, jpeg_quality, png_quality):
+        def __init__(
+                self, jobs, optimize, jpeg_quality, png_quality, jb2lossy):
             self.jobs = jobs
             self.optimize = optimize
             self.jpeg_quality = jpeg_quality
             self.png_quality = png_quality
             self.jbig2_page_group_size = 0
+            self.jbig2_lossy = jb2lossy
 
     logging.basicConfig(level=logging.DEBUG)
     log = logging.getLogger()
@@ -416,7 +417,8 @@ def main(infile, outfile, level, jobs=1):
         jobs=jobs,
         optimize=int(level),
         jpeg_quality=0,  # Use default
-        png_quality=0
+        png_quality=0,
+        jb2lossy=False
     )
     ctx.set_options(options)
 
diff --git a/tests/test_optimize.py b/tests/test_optimize.py
index a232f5a7..fa1072cf 100644
--- a/tests/test_optimize.py
+++ b/tests/test_optimize.py
@@ -64,19 +64,22 @@ def test_jpg_png_params(resources, outpdf, spoof_tesseract_noop):
 
 
 @pytest.mark.skipif(not jbig2enc.available(), reason='need jbig2enc')
-@pytest.mark.parametrize('optimize', ['2', '3'])
-def test_jbig2(optimize, resources, outpdf, spoof_tesseract_noop):
-    check_ocrmypdf(
+@pytest.mark.parametrize('lossy', [False, True])
+def test_jbig2_lossy(lossy, resources, outpdf, spoof_tesseract_noop):
+    args = [
         resources / 'ccitt.pdf', outpdf, '--image-dpi', '200',
-        '--optimize', optimize, '--jpg-quality', '50', '--png-quality', '20',
-        env=spoof_tesseract_noop
-    )
+        '--optimize', 3, '--jpg-quality', '50', '--png-quality', '20'
+    ]
+    if lossy:
+        args.append('--jbig2-lossy')
+
+    check_ocrmypdf(*args, env=spoof_tesseract_noop)
 
     pdf = pikepdf.open(outpdf)
     pim = pikepdf.PdfImage(next(iter(pdf.pages[0].images.values())))
     assert pim.filters[0] == '/JBIG2Decode'
 
-    if optimize == '3':
+    if lossy:
         assert '/JBIG2Globals' in pim.decode_parms[0]
     else:
         assert len(pim.decode_parms) == 0