diff --git a/.circleci/config.yml b/.circleci/config.yml
index afa396fa..31520991 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -33,6 +33,12 @@ common: &common
             set +x
           fi
 jobs:
+  py37-coveragepy5:
+    <<: *common
+    docker:
+      - image: circleci/python:3.7
+        environment:
+          TOXENV=py37-coveragepy5-coverage
   py37:
     <<: *common
     docker:
@@ -80,6 +86,7 @@ workflows:
   version: 2
   test:
     jobs:
+      - py37-coveragepy5
       - py37
       - py37-click6
       - py36
diff --git a/covimerage/__init__.py b/covimerage/__init__.py
index 0f0ad14f..c7fd63a4 100755
--- a/covimerage/__init__.py
+++ b/covimerage/__init__.py
@@ -186,14 +186,25 @@ def get_coveragepy_data(self):
 
     # TODO: move to CoverageWrapper
     def write_coveragepy_data(self, data_file='.coverage'):
+        import coverage
+
         cov_data = self.get_coveragepy_data()
-        if not cov_data.line_counts():
+        try:
+            line_counts = cov_data.line_counts()
+        except AttributeError:
+            line_counts = coverage.data.line_counts(cov_data)
+        if not line_counts:
             logger.warning('Not writing coverage file: no data to report!')
             return False
 
         if isinstance(data_file, string_types):
             logger.info('Writing coverage file %s.', data_file)
-            cov_data.write_file(data_file)
+            try:
+                write_file = cov_data.write_file
+            except AttributeError:
+                # coveragepy 5
+                write_file = cov_data._write_file
+            write_file(data_file)
         else:
             try:
                 filename = data_file.name
diff --git a/covimerage/coveragepy.py b/covimerage/coveragepy.py
index 7e32e1af..a929de48 100644
--- a/covimerage/coveragepy.py
+++ b/covimerage/coveragepy.py
@@ -13,27 +13,42 @@
     r'"\s*(pragma|PRAGMA)[:\s]?\s*(no|NO)\s*(cover|COVER)')
 
 
+try:
+    from coverage.data import CoverageJsonData as CoveragePyData
+except ImportError:
+    from coverage.data import CoverageData as CoveragePyData
+
+
 @attr.s(frozen=True)
 class CoverageData(object):
     cov_data = attr.ib(default=None)
     data_file = attr.ib(default=None)
 
     def __attrs_post_init__(self):
-        if self.cov_data and self.data_file:
-            raise TypeError('data and data_file are mutually exclusive.')
-        if self.cov_data:
-            if not isinstance(self.cov_data, coverage.data.CoverageData):
-                raise TypeError(
-                    'data needs to be of type coverage.data.CoverageData')
+        if self.cov_data is not None:
+            if not isinstance(self.cov_data, CoveragePyData):
+                raise TypeError('data needs to be of type %s.%s' % (
+                    CoveragePyData.__module__,
+                    CoveragePyData.__name__,))
+            if self.data_file is not None:
+                raise TypeError('data and data_file are mutually exclusive.')
             return
-        cov_data = coverage.data.CoverageData()
+        cov_data = CoveragePyData()
         if self.data_file:
             fname, fobj, fstr = get_fname_and_fobj_and_str(self.data_file)
             try:
                 if fobj:
-                    cov_data.read_fileobj(fobj)
+                    try:
+                        read_fileobj = cov_data.read_fileobj
+                    except AttributeError:  # made private in coveragepy 5
+                        read_fileobj = cov_data._read_fileobj
+                    read_fileobj(fobj)
                 else:
-                    cov_data.read_file(fname)
+                    try:
+                        read_file = cov_data.read_file
+                    except AttributeError:  # made private in coveragepy 5
+                        read_file = cov_data._read_file
+                    read_file(fname)
             except coverage.CoverageException as exc:
                 raise CoverageWrapperException(
                     'Coverage could not read data_file: %s' % fstr,
@@ -73,6 +88,8 @@ def __attrs_post_init__(self):
         if not isinstance(self.data, CoverageData):
             data = CoverageData(cov_data=self.data, data_file=self.data_file)
             object.__setattr__(self, 'data', data)
+            # (confusing to have it twice)
+            # object.__setattr__(self, 'data_file', None)
         elif self.data_file:
             raise TypeError('data and data_file are mutually exclusive.')
 
@@ -96,7 +113,12 @@ def _get_file_reporter(self, morf):
             config_file=True if self.config_file is None else self.config_file,
         )
         cov_coverage._init()
-        cov_coverage.data = self.data.cov_data
+        if hasattr(cov_coverage, '_data'):
+            # coveragepy 5
+            # TODO: get rid of intermediate handling of CoverageData?
+            cov_coverage._data = self.data.cov_data
+        else:
+            cov_coverage.data = self.data.cov_data
         return cov_coverage
 
     @handle_coverage_exceptions
diff --git a/setup.py b/setup.py
index 72bd54b3..30997d7e 100755
--- a/setup.py
+++ b/setup.py
@@ -84,7 +84,7 @@ def run(self):
     install_requires=[
         'attrs',
         'click',
-        'coverage<=5',
+        'coverage',
     ],
     extras_require={
         'testing': DEPS_TESTING,
diff --git a/tests/test_cli.py b/tests/test_cli.py
index 77abe356..b39fe9e7 100644
--- a/tests/test_cli.py
+++ b/tests/test_cli.py
@@ -410,6 +410,7 @@ def test_coverage_plugin_for_annotate_merged_conditionals(runner, capfd,
         f.write('[run]\nplugins = covimerage')
 
     exit_code = call(['env', 'COVERAGE_FILE=%s' % tmpfile,
+                      'COVERAGE_STORAGE=json',  # for coveragepy 5
                       'coverage', 'annotate', '--rcfile', coveragerc,
                       '--directory', str(tmpdir)])
     out, err = capfd.readouterr()
diff --git a/tests/test_coveragepy.py b/tests/test_coveragepy.py
index 9dedfedf..9b04d56d 100644
--- a/tests/test_coveragepy.py
+++ b/tests/test_coveragepy.py
@@ -60,20 +60,32 @@ def coverage_fileobj():
 
 def test_coveragedata(coverage_fileobj):
     import coverage
-    from covimerage.coveragepy import CoverageData, CoverageWrapperException
+    from covimerage.coveragepy import (
+        CoverageData, CoveragePyData, CoverageWrapperException)
 
     with pytest.raises(TypeError) as excinfo:
-        CoverageData(data_file='foo', cov_data='bar')
+        CoverageData(data_file='foo', cov_data=CoveragePyData())
     assert excinfo.value.args == (
         'data and data_file are mutually exclusive.',)
 
     data = CoverageData()
-    assert isinstance(data.cov_data, coverage.data.CoverageData)
+    try:
+        from coverage.data import CoverageJsonData
+    except ImportError:
+        assert isinstance(data.cov_data, coverage.data.CoverageData)
+    else:
+        assert isinstance(data.cov_data, CoverageJsonData)
 
     with pytest.raises(TypeError) as excinfo:
         CoverageData(cov_data='foo')
-    assert excinfo.value.args == (
-        'data needs to be of type coverage.data.CoverageData',)
+    try:
+        from coverage.data import CoverageJsonData
+    except ImportError:
+        assert excinfo.value.args == (
+            'data needs to be of type coverage.data.CoverageData',)
+    else:
+        assert excinfo.value.args == (
+            'data needs to be of type coverage.data.CoverageJsonData',)
 
     with pytest.raises(CoverageWrapperException) as excinfo:
         CoverageData(data_file='/does/not/exist')
@@ -106,7 +118,12 @@ def test_coveragedata_empty(covdata_empty):
 
     f = StringIO()
     data = CoverageData()
-    data.cov_data.write_fileobj(f)
+    try:
+        write_fileobj = data.cov_data.write_fileobj
+    except AttributeError:
+        # coveragepy 5
+        write_fileobj = data.cov_data._write_fileobj
+    write_fileobj(f)
     f.seek(0)
     assert f.read() == covdata_empty
 
@@ -114,13 +131,13 @@ def test_coveragedata_empty(covdata_empty):
 def test_coveragewrapper(coverage_fileobj, devnull):
     import coverage
     from covimerage.coveragepy import (
-        CoverageData, CoverageWrapper, CoverageWrapperException)
+        CoverageData, CoveragePyData, CoverageWrapper, CoverageWrapperException)
 
     cov_data = CoverageWrapper()
     assert cov_data.lines == {}
     assert isinstance(cov_data.data, CoverageData)
 
-    cov_data = CoverageWrapper(data=coverage.data.CoverageData())
+    cov_data = CoverageWrapper(data=CoveragePyData())
     assert cov_data.lines == {}
     assert isinstance(cov_data.data, CoverageData)
 
@@ -128,7 +145,7 @@ def test_coveragewrapper(coverage_fileobj, devnull):
         CoverageWrapper(data_file='foo', data='bar')
 
     with pytest.raises(TypeError):
-        CoverageWrapper(data_file='foo', data=CoverageData())
+        CoverageWrapper(data_file='foo', data=CoveragePyData())
 
     cov = CoverageWrapper(data_file=coverage_fileobj)
     with pytest.raises(attr.exceptions.FrozenInstanceError):
@@ -139,7 +156,11 @@ def test_coveragewrapper(coverage_fileobj, devnull):
             3, 8, 9, 11, 13, 14, 15, 17, 23]}
 
     assert isinstance(cov._cov_obj, coverage.control.Coverage)
-    assert cov._cov_obj.data is cov.data.cov_data
+    if hasattr(cov._cov_obj, '_data'):
+        # coveragepy 5
+        assert cov._cov_obj._data is cov.data.cov_data
+    else:
+        assert cov._cov_obj.data is cov.data.cov_data
 
     with pytest.raises(CoverageWrapperException) as excinfo:
         CoverageWrapper(data_file=devnull.name)
@@ -158,6 +179,17 @@ def test_coveragewrapper(coverage_fileobj, devnull):
         e.message, e.orig_exc)
 
 
+def test_coveragewrapper_requires_jsondata():
+    pytest.importorskip('coverage.sqldata')
+    from covimerage.coveragepy import CoverageWrapper
+
+    with pytest.raises(TypeError) as excinfo:
+        CoverageWrapper(data=coverage.sqldata.CoverageSqliteData())
+
+    assert excinfo.value.args[0] == (
+        'data needs to be of type coverage.data.CoverageJsonData')
+
+
 def test_coveragewrapper_uses_config_file(tmpdir, capfd):
     from covimerage.coveragepy import CoverageWrapper, CoverageWrapperException
 
diff --git a/tests/test_main.py b/tests/test_main.py
index 5733ba09..06bd5a7b 100644
--- a/tests/test_main.py
+++ b/tests/test_main.py
@@ -380,8 +380,12 @@ def test_merged_profiles_get_coveragepy_data():
 
     m = MergedProfiles([])
     cov_data = m.get_coveragepy_data()
-    assert isinstance(cov_data, coverage.CoverageData)
-    assert repr(cov_data) == '<CoverageData lines={0} arcs=None tracers={0} runs=[0]>'
+    try:
+        from coverage.data import CoverageJsonData
+    except ImportError:
+        assert isinstance(cov_data, coverage.CoverageData)
+    else:
+        assert isinstance(cov_data, CoverageJsonData)
 
 
 def test_merged_profiles_write_coveragepy_data_handles_fname_and_fobj(
diff --git a/tox.ini b/tox.ini
index 24ba57e9..bdddbf15 100644
--- a/tox.ini
+++ b/tox.ini
@@ -13,6 +13,8 @@ changedir =
   integration: {envtmpdir}
 deps =
   click6: click<7
+  coveragepy4: coverage<5
+  coveragepy5: coverage>=5<6
 
 [testenv:checkqa]
 extras = qa