diff --git a/IMPLEMENTATION_COVERAGE.md b/IMPLEMENTATION_COVERAGE.md
index 688ab57d8..1d9811983 100644
--- a/IMPLEMENTATION_COVERAGE.md
+++ b/IMPLEMENTATION_COVERAGE.md
@@ -815,16 +815,16 @@
 - [ ] update_user_profile
 
 ## cognito-identity - 0% implemented
-- [ ] create_identity_pool
+- [X] create_identity_pool
 - [ ] delete_identities
 - [ ] delete_identity_pool
 - [ ] describe_identity
 - [ ] describe_identity_pool
-- [ ] get_credentials_for_identity
-- [ ] get_id
+- [X] get_credentials_for_identity
+- [X] get_id
 - [ ] get_identity_pool_roles
-- [ ] get_open_id_token
-- [ ] get_open_id_token_for_developer_identity
+- [X] get_open_id_token
+- [X] get_open_id_token_for_developer_identity
 - [ ] list_identities
 - [ ] list_identity_pools
 - [ ] lookup_developer_identity
diff --git a/moto/cognitoidentity/models.py b/moto/cognitoidentity/models.py
index daa2a4641..c916b7f62 100644
--- a/moto/cognitoidentity/models.py
+++ b/moto/cognitoidentity/models.py
@@ -95,6 +95,15 @@ class CognitoIdentityBackend(BaseBackend):
             })
         return response
 
+    def get_open_id_token(self, identity_id):
+        response = json.dumps(
+            {
+                "IdentityId": identity_id,
+                "Token": get_random_identity_id(self.region)
+            }
+        )
+        return response
+
 
 cognitoidentity_backends = {}
 for region in boto.cognito.identity.regions():
diff --git a/moto/cognitoidentity/responses.py b/moto/cognitoidentity/responses.py
index e7b428329..33faaa300 100644
--- a/moto/cognitoidentity/responses.py
+++ b/moto/cognitoidentity/responses.py
@@ -35,3 +35,8 @@ class CognitoIdentityResponse(BaseResponse):
         return cognitoidentity_backends[self.region].get_open_id_token_for_developer_identity(
             self._get_param('IdentityId') or get_random_identity_id(self.region)
         )
+
+    def get_open_id_token(self):
+        return cognitoidentity_backends[self.region].get_open_id_token(
+            self._get_param("IdentityId") or get_random_identity_id(self.region)
+        )
diff --git a/moto/server.py b/moto/server.py
index 5ad02d383..971589cac 100644
--- a/moto/server.py
+++ b/moto/server.py
@@ -21,6 +21,16 @@ from moto.core.utils import convert_flask_to_httpretty_response
 HTTP_METHODS = ["GET", "POST", "PUT", "DELETE", "HEAD", "PATCH"]
 
 
+DEFAULT_SERVICE_REGION = ('s3', 'us-east-1')
+
+# Map of unsigned calls to service-region as per AWS API docs
+# https://docs.aws.amazon.com/cognito/latest/developerguide/resource-permissions.html#amazon-cognito-signed-versus-unsigned-apis
+UNSIGNED_REQUESTS = {
+    'AWSCognitoIdentityService': ('cognito-identity', 'us-east-1'),
+    'AWSCognitoIdentityProviderService': ('cognito-idp', 'us-east-1'),
+}
+
+
 class DomainDispatcherApplication(object):
     """
     Dispatch requests to different applications based on the "Host:" header
@@ -50,6 +60,32 @@ class DomainDispatcherApplication(object):
 
         raise RuntimeError('Invalid host: "%s"' % host)
 
+    def infer_service_region(self, environ):
+        auth = environ.get('HTTP_AUTHORIZATION')
+        if auth:
+            # Signed request
+            # Parse auth header to find service assuming a SigV4 request
+            # https://docs.aws.amazon.com/general/latest/gr/sigv4-signed-request-examples.html
+            # ['Credential=sdffdsa', '20170220', 'us-east-1', 'sns', 'aws4_request']
+            try:
+                credential_scope = auth.split(",")[0].split()[1]
+                _, _, region, service, _ = credential_scope.split("/")
+                return service, region
+            except ValueError:
+                # Signature format does not match, this is exceptional and we can't
+                # infer a service-region. A reduced set of services still use
+                # the deprecated SigV2, ergo prefer S3 as most likely default.
+                # https://docs.aws.amazon.com/general/latest/gr/signature-version-2.html
+                return DEFAULT_SERVICE_REGION
+        else:
+            # Unsigned request
+            target = environ.get('HTTP_X_AMZ_TARGET')
+            if target:
+                service, _ = target.split('.', 1)
+                return UNSIGNED_REQUESTS.get(service, DEFAULT_SERVICE_REGION)
+            # S3 is the last resort when the target is also unknown
+            return DEFAULT_SERVICE_REGION
+
     def get_application(self, environ):
         path_info = environ.get('PATH_INFO', '')
 
@@ -66,19 +102,7 @@ class DomainDispatcherApplication(object):
         else:
             host = environ['HTTP_HOST'].split(':')[0]
         if host in {'localhost', 'motoserver'} or host.startswith("192.168."):
-            # Fall back to parsing auth header to find service
-            # ['Credential=sdffdsa', '20170220', 'us-east-1', 'sns', 'aws4_request']
-            try:
-                _, _, region, service, _ = environ['HTTP_AUTHORIZATION'].split(",")[0].split()[
-                    1].split("/")
-            except (KeyError, ValueError):
-                # Some cognito-idp endpoints (e.g. change password) do not receive an auth header.
-                if environ.get('HTTP_X_AMZ_TARGET', '').startswith('AWSCognitoIdentityProviderService'):
-                    service = 'cognito-idp'
-                else:
-                    service = 's3'
-
-                region = 'us-east-1'
+            service, region = self.infer_service_region(environ)
             if service == 'dynamodb':
                 if environ['HTTP_X_AMZ_TARGET'].startswith('DynamoDBStreams'):
                     host = 'dynamodbstreams'
diff --git a/tests/test_cognitoidentity/test_cognitoidentity.py b/tests/test_cognitoidentity/test_cognitoidentity.py
index ac79fa223..ea9ccbc78 100644
--- a/tests/test_cognitoidentity/test_cognitoidentity.py
+++ b/tests/test_cognitoidentity/test_cognitoidentity.py
@@ -68,7 +68,7 @@ def test_get_open_id_token_for_developer_identity():
         },
         TokenDuration=123
     )
-    assert len(result['Token'])
+    assert len(result['Token']) > 0
     assert result['IdentityId'] == '12345'
 
 @mock_cognitoidentity
@@ -83,3 +83,15 @@ def test_get_open_id_token_for_developer_identity_when_no_explicit_identity_id()
     )
     assert len(result['Token']) > 0
     assert len(result['IdentityId']) > 0
+
+@mock_cognitoidentity
+def test_get_open_id_token():
+    conn = boto3.client('cognito-identity', 'us-west-2')
+    result = conn.get_open_id_token(
+        IdentityId='12345',
+        Logins={
+            'someurl': '12345'
+        }
+    )
+    assert len(result['Token']) > 0
+    assert result['IdentityId'] == '12345'