diff --git a/.travis.yml b/.travis.yml
index d3b328ae..2575bd0f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,10 +9,6 @@ cache:
 
 matrix:
   include:
-    - os: linux
-      sudo: required
-      language: python
-      python: 3.4
     - os: linux
       sudo: required
       language: python
diff --git a/RELEASE_NOTES.rst b/RELEASE_NOTES.rst
index edcfc01b..58292eb1 100644
--- a/RELEASE_NOTES.rst
+++ b/RELEASE_NOTES.rst
@@ -3,6 +3,13 @@ RELEASE NOTES
 
 OCRmyPDF uses `semantic versioning <http://semver.org/>`_.
 
+next
+====
+
+-   Python 3.4 compatibility dropped
+-   Remove deprecated API functions: ocrmypdf.main
+-   Remove OCRmyPDF.sh script
+
 
 v4.5.3
 ======
diff --git a/docs/installation.rst b/docs/installation.rst
index 6f8c540f..761d2d2d 100644
--- a/docs/installation.rst
+++ b/docs/installation.rst
@@ -139,7 +139,7 @@ Install or upgrade the required Homebrew packages, if any are missing:
    brew install libxml2 libffi leptonica
    brew install unpaper   # optional
    
-Python 3.4, 3.5 and 3.6 are supported.
+Python 3.5 and 3.6 are supported.
 
 Install the required Tesseract OCR engine with the language packs you plan to use:
    
@@ -290,7 +290,7 @@ where /c/Users/sampleuser is a Unix representation of the Windows path C:\\Users
 Installing HEAD revision from sources
 -------------------------------------
 
-If you have ``git`` and Python 3.4 or newer installed, you can install from source. When the ``pip`` installer runs,
+If you have ``git`` and Python 3.5 or newer installed, you can install from source. When the ``pip`` installer runs,
 it will alert you if dependencies are missing.
 
 To install the HEAD revision from sources in the current Python 3 environment:
diff --git a/ocrmypdf/pageinfo.py b/ocrmypdf/pageinfo.py
index a54ec385..4b558f58 100644
--- a/ocrmypdf/pageinfo.py
+++ b/ocrmypdf/pageinfo.py
@@ -9,13 +9,6 @@ import sys
 import PyPDF2 as pypdf
 from collections import namedtuple
 
-try:
-    from math import isclose
-except ImportError:
-    def isclose(a, b, rel_tol=1e-9):
-        "Python 3.4 does not have math.isclose()"
-        diff = abs(b - a)
-        return diff <= abs(rel_tol * b) or diff <= abs(rel_tol * a)
 
 matrix_mult = pypdf.pdf.utils.matrixMultiply
 
diff --git a/ocrmypdf/pdfa.py b/ocrmypdf/pdfa.py
index c06df910..b10262f8 100644
--- a/ocrmypdf/pdfa.py
+++ b/ocrmypdf/pdfa.py
@@ -122,10 +122,6 @@ def generate_pdfa_ps(target_filename, pdfmark, icc='sRGB'):
         f.write(ps)
 
 
-# The old name is generate_pdfa_def -- now deprecated
-generate_pdfa_def = generate_pdfa_ps
-
-
 def file_claims_pdfa(filename):
     """Determines if the file claims to be PDF/A compliant
 
diff --git a/tests/test_main.py b/tests/test_main.py
index 2997763e..2adfa578 100644
--- a/tests/test_main.py
+++ b/tests/test_main.py
@@ -571,7 +571,6 @@ def test_non_square_resolution(renderer, spoof_tesseract_cache,
     assert in_pageinfo[0]['yres'] == out_pageinfo[0]['yres']
 
 
-@pytest.mark.skipif(sys.version_info < (3, 5), reason="needs math.isclose")
 @pytest.mark.parametrize('renderer', [
     'hocr',
     'tesseract'
@@ -814,7 +813,6 @@ def test_form_xobject(spoof_tesseract_noop, resources, outpdf):
                    env=spoof_tesseract_noop)
 
 
-@pytest.mark.skipif(sys.version_info < (3, 5), reason="needs math.isclose")
 @pytest.mark.parametrize('renderer', [
     'hocr',
     'tesseract',
diff --git a/tests/test_pageinfo.py b/tests/test_pageinfo.py
index dcb4ab90..0f70b1a4 100644
--- a/tests/test_pageinfo.py
+++ b/tests/test_pageinfo.py
@@ -35,7 +35,6 @@ def test_single_page_text(outdir):
     assert len(page['images']) == 0
 
 
-@pytest.mark.skipif(sys.version_info < (3, 5), reason="needs Path.read_bytes")
 def test_single_page_image(outdir):
     filename = outdir / 'image-mono.pdf'