diff --git a/.appveyor.yml b/.appveyor.yml
index 3970cef8f..93b1cf942 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -5,7 +5,7 @@ environment:
           PACKAGES: "cython numpy matplotlib-base proj4 pykdtree scipy"
         - PYTHON_VERSION: "2.7"
           CONDA_INSTALL_LOCN: "C:\\Miniconda-x64"
-          PACKAGES: "cython=0.17 numpy=1.10.0 matplotlib=1.5.1 nose proj4=4.9.1 scipy=0.16.0 mock msinttypes futures"
+          PACKAGES: "cython numpy=1.10.0 matplotlib=1.5.1 nose proj4=4.9.1 scipy=0.16.0 mock msinttypes futures"
 
 install:
   # Install miniconda
diff --git a/INSTALL b/INSTALL
index 5f11acf25..93594ccd6 100644
--- a/INSTALL
+++ b/INSTALL
@@ -56,7 +56,7 @@ The recipes for these can be found at https://github.com/conda-forge/feedstocks.
 **Python** 2.7 or later (https://www.python.org/)
     Cartopy requires Python 2.7 or later.
 
-**Cython** 0.29 or later (https://pypi.python.org/pypi/Cython/)
+**Cython** 0.28 or later (https://pypi.python.org/pypi/Cython/)
 
 **NumPy** 1.10 or later (http://www.numpy.org/)
     Python package for scientific computing including a powerful N-dimensional
diff --git a/lib/cartopy/trace.pyx b/lib/cartopy/trace.pyx
index c1d8d5a89..305feea02 100644
--- a/lib/cartopy/trace.pyx
+++ b/lib/cartopy/trace.pyx
@@ -1,4 +1,4 @@
-# (C) British Crown Copyright 2011 - 2018, Met Office
+# (C) British Crown Copyright 2011 - 2019, Met Office
 #
 # This file is part of cartopy.
 #
@@ -170,7 +170,7 @@ cdef class LineAccumulator:
                                                &geoms[0], geoms.size())
         return geom
 
-    cdef list[Line].size_type size(self):
+    cdef size_t size(self):
         return self.lines.size()
 
 
diff --git a/setup.py b/setup.py
index 5f53fb33d..445c5ce4f 100644
--- a/setup.py
+++ b/setup.py
@@ -1,4 +1,4 @@
-# (C) British Crown Copyright 2011 - 2018, Met Office
+# (C) British Crown Copyright 2011 - 2019, Met Office
 #
 # This file is part of cartopy.
 #
@@ -43,9 +43,9 @@
 
 if not IS_SDIST:
     import Cython
-    if Cython.__version__ < '0.29':
+    if Cython.__version__ < '0.28':
         raise ImportError(
-            "Cython 0.29+ is required to install cartopy from source.")
+            "Cython 0.28+ is required to install cartopy from source.")
 
     from Cython.Distutils import build_ext as cy_build_ext