diff --git a/.travis.yml b/.travis.yml
index bf630a5..ad05a89 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,7 +1,6 @@
-# We only use Python for coveralls; both Python 2.7 and 3.6 are
-# tested but that is done within docker containers
+# We only use Python for coveralls
 language: python
-python: 3.6
+python: 3.7
 
 services:
     - docker
diff --git a/Dockerfile b/Dockerfile
index 4810b50..97409db 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -1,4 +1,4 @@
-FROM python:3.6
+FROM python:3.7
 
 VOLUME /opt
 WORKDIR /opt
diff --git a/Makefile b/Makefile
index 3c8f97e..86b155c 100644
--- a/Makefile
+++ b/Makefile
@@ -1,4 +1,4 @@
-.PHONY: attach build build_tester clean coverage create_network docs psql release_pypi release_pypitest release_quay remove_network start_postgres stop_postgres test test_one_pg_version test27 test36 view_docs wait_for_postgres
+.PHONY: attach build build_tester clean coverage create_network docs psql release_pypi release_pypitest release_quay remove_network start_postgres stop_postgres test test_one_pg_version pytest view_docs wait_for_postgres
 
 SUPPORTED_PG_VERSIONS ?= 9.5.13 9.6.4 10.4
 # The default Postgres that will be used in individual targets
@@ -26,15 +26,10 @@ build: clean
         .
 
 build_tester:
-	@echo "Building the tester27 and tester36 docker images"
+	@echo "Building the tester docker image"
 	docker build . \
         -f tests/Dockerfile \
-        --build-arg PYTHON_VERSION=2.7 \
-        -t tester27
-	docker build . \
-        -f tests/Dockerfile \
-        --build-arg PYTHON_VERSION=3.6 \
-        -t tester36
+        -t tester
 
 clean:
 	@echo "Cleaning the repo"
@@ -94,7 +89,7 @@ stop_postgres:
 	@echo "Stopping postgres (if it is running)"
 	@-docker stop $(POSTGRES_HOST) || true
 
-test_one_pg_version: start_postgres wait_for_postgres test27 test36 remove_network clean
+test_one_pg_version: start_postgres wait_for_postgres pytest remove_network clean
 
 test: clean build_tester
 	@for pg_version in ${SUPPORTED_PG_VERSIONS}; do \
@@ -102,25 +97,15 @@ test: clean build_tester
         $(MAKE) test_one_pg_version POSTGRES_VERSION="$$pg_version"; \
     done
 
-test27:
-	@echo "Running pytest with Python 2.7"
-	@docker run \
-        --rm \
-        -e WITHIN_DOCKER_FLAG=true \
-        -e POSTGRES_PORT=5432 \
-        -v $(shell pwd):/opt \
-        --net=$(COMPOSED_NETWORK) \
-        tester27
-
-test36:
-	@echo "Running pytest with Python 3.6"
+pytest:
+	@echo "Running pytest"
 	@docker run \
         --rm \
         -e WITHIN_DOCKER_FLAG=true \
         -e POSTGRES_PORT=5432 \
         -v $(shell pwd):/opt \
         --net=$(COMPOSED_NETWORK) \
-        tester36
+        tester
 
 wait_for_postgres:
 	@echo 'Sleeping while postgres starts up';
diff --git a/pgbedrock/attributes.py b/pgbedrock/attributes.py
index a53181b..39ad178 100644
--- a/pgbedrock/attributes.py
+++ b/pgbedrock/attributes.py
@@ -1,6 +1,8 @@
 import copy
 import datetime as dt
 import hashlib
+import hmac
+import base64
 import logging
 
 import click
@@ -87,6 +89,14 @@ def create_md5_hash(rolename, value):
     salted_input = (value + rolename).encode('utf-8')
     return 'md5' + hashlib.md5(salted_input).hexdigest()
 
+def create_scram_hash(password, salt, iterations):
+    digest = hashlib.pbkdf2_hmac("sha256", password.encode(), salt, iterations)
+    client_key = hmac.digest(digest, "Client Key".encode(), hashlib.sha256)
+    stored_key = base64.b64encode(hashlib.sha256(client_key).digest()).decode()
+    server_key = base64.b64encode(hmac.digest(digest, "Server Key".encode(), hashlib.sha256)).decode()
+
+    return "SCRAM-SHA-256${}:{}${}:{}".format(iterations, base64.b64encode(salt).decode(), stored_key, server_key)
+
 
 def is_valid_forever(val):
     if val is None or val == 'infinity':
@@ -194,13 +204,47 @@ def get_attribute_value(self, attribute):
         return value
 
     def is_same_password(self, value):
-        """ Convert the input value into a postgres rolname-salted md5 hash and compare
-        it with the currently stored hash """
-        if value is None:
-            return self.current_attributes.get('rolpassword') is None
+        """ Compare stored password hash to the new password.
+
+        Returns ``True`` if both ``value`` and the stored password are ``None`` (empty)
+        **or** ``value`` is a plain text password its hash matches the stored password
+        hash **or** ``value`` is a hashed password and matches the stored password hash
+        type and value. ``False`` in any other case. """
+        current_value = self.current_attributes.get('rolpassword')
+
+        if value is None or current_value is None:
+            return value == current_value
+
+        if hmac.compare_digest(current_value, value):
+            return True
+
+        if current_value.startswith("SCRAM-SHA-256$"):
+            if value.startswith("md5"):
+                return False
+
+            if value.startswith("SCRAM-SHA-256$"):
+                return hmac.compare_digest(current_value, value)
+
+            hash_parts = current_value.split("$")
+
+            iterations, salt = hash_parts[1].split(":")
+            iterations = int(iterations)
+            salt = base64.b64decode(salt)
+
+            return hmac.compare_digest(current_value, create_scram_hash(value, salt, iterations))
+
+        if current_value.startswith("md5"):
+            if value.startswith("SCRAM-SHA-256$"):
+                return False
+
+            if value.startswith("md5"):
+                return hmac.compare_digest(current_value, value)
+
+            return hmac.compare_digest(current_value, create_md5_hash(self.rolename, value))
 
-        md5_hash = create_md5_hash(self.rolename, value)
-        return self.current_attributes.get('rolpassword') == md5_hash
+        # There’s currently only two hash algorithm supported by Postgres (md5
+        # and SCRAM-SHA-256) so we should never reach this.
+        return False
 
     def role_exists(self):
         # If current_attributes is empty then the rolname wasn't in pg_authid, i.e. it doesn't exist
diff --git a/requirements-dev.txt b/requirements-dev.txt
index 16b680f..ee3c7ef 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -2,3 +2,4 @@ pytest==3.1.3
 pytest-cov==2.5.1
 -r requirements-docs.txt
 wheel==0.33.6
+psycopg2==2.7.7
diff --git a/requirements.txt b/requirements.txt
index 4fcc6a0..f808bfe 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,6 +1,6 @@
 Cerberus==1.1
 click==6.7
 Jinja2==2.10.1
-MarkupSafe==1.0
+MarkupSafe==1.1.1
 psycopg2==2.7.3
 PyYAML==5.2
diff --git a/setup.py b/setup.py
index de26ed4..8528fb1 100644
--- a/setup.py
+++ b/setup.py
@@ -42,9 +42,7 @@ def get_version():
     install_requires=required,
     classifiers=[
         'Programming Language :: Python',
-        'Programming Language :: Python :: 2',
         'Programming Language :: Python :: 3',
-        'Programming Language :: Python :: 2.7',
-        'Programming Language :: Python :: 3.6',
+        'Programming Language :: Python :: 3.7',
     ],
 )
diff --git a/tests/Dockerfile b/tests/Dockerfile
index 9913906..cb8ce9a 100644
--- a/tests/Dockerfile
+++ b/tests/Dockerfile
@@ -1,5 +1,4 @@
-ARG PYTHON_VERSION
-FROM python:$PYTHON_VERSION
+FROM python:3.7
 
 VOLUME /opt
 WORKDIR /opt
diff --git a/tests/test_attributes.py b/tests/test_attributes.py
index 7688786..921b46d 100644
--- a/tests/test_attributes.py
+++ b/tests/test_attributes.py
@@ -382,14 +382,38 @@ def test_set_attribute_value_valid_until(roleconf):
     rolpassword=attr.create_md5_hash(ROLE1, 'supersecret'),
 ))
 @pytest.mark.parametrize('desired_value, expected', [
-    ('supersecret', True),
-    ('incorrect_password', False)])
-def test_is_same_password(roleconf, desired_value, expected):
+        ('supersecret', True),
+        ('md5c85aa4317b187e73a31e8ab775a10833', True),
+        ('incorrect_password', False),
+        ('SCRAM-SHA-256$4096:c3VwZXJzYWx0$E6lZT4K2olotsu19xYcF825iMPGdJQDYaklVS2mR6js=:Pe9DLNf8idnP59Q5l8Xmz3H+6LrTuiq//bcujQPGsRM=', False),
+    ]
+)
+def test_is_same_password_md5(roleconf, desired_value, expected):
     assert roleconf.is_same_password(desired_value) == expected
 
 
-def test_is_same_password_if_empty(roleconf):
-    assert roleconf.is_same_password(None) is True
+@nondefault_attributes(dict(
+    rolpassword=attr.create_scram_hash('supersecret', 'supersalt'.encode(), 4096),
+))
+@pytest.mark.parametrize('desired_value, expected', [
+        ('supersecret', True),
+        ('SCRAM-SHA-256$4096:c3VwZXJzYWx0$E6lZT4K2olotsu19xYcF825iMPGdJQDYaklVS2mR6js=:Pe9DLNf8idnP59Q5l8Xmz3H+6LrTuiq//bcujQPGsRM=', True),
+        ('incorrect_password', False),
+        ('md5c85aa4317b187e73a31e8ab775a10833', False),
+    ]
+)
+def test_is_same_password_scram(roleconf, desired_value, expected):
+    assert roleconf.is_same_password(desired_value) == expected
+
+@pytest.mark.parametrize('desired_value, expected', [
+        (None, True),
+        ('incorrect_password', False),
+        ('md5c85aa4317b187e73a31e8ab775a10833', False),
+        ('SCRAM-SHA-256$4096:c3VwZXJzYWx0$E6lZT4K2olotsu19xYcF825iMPGdJQDYaklVS2mR6js=:Pe9DLNf8idnP59Q5l8Xmz3H+6LrTuiq//bcujQPGsRM=', False),
+    ]
+)
+def test_is_same_password_if_empty(roleconf, desired_value, expected):
+    assert roleconf.is_same_password(desired_value) == expected
 
 
 @nondefault_attributes(dict(