diff --git a/annif/exception.py b/annif/exception.py
index 867eb2beb..9acbd052b 100644
--- a/annif/exception.py
+++ b/annif/exception.py
@@ -6,29 +6,19 @@
 
 class AnnifException(ClickException):
     """Base Annif exception. We define this as a subclass of ClickException so
-    that the CLI can automatically handle exceptions."""
+    that the CLI can automatically handle exceptions. This exception cannot be
+    instantiated directly - subclasses should be used instead."""
 
     def __init__(self, message, project_id=None, backend_id=None):
         super().__init__(message)
         self.project_id = project_id
         self.backend_id = backend_id
 
-    def format_message(self):
-        if self.project_id is not None:
-            return "Project '{}': {}".format(self.project_id,
-                                             self.message)
-        if self.backend_id is not None:
-            return "Backend '{}': {}".format(self.backend_id,
-                                             self.message)
-        return "Error: {}".format(self.message)
-
-
-class NotInitializedException(AnnifException):
-    """Exception raised for attempting to use a project or backend that
-    cannot be initialized, most likely since it is not yet functional
-    because of lack of vocabulary or training."""
+        if self.prefix is None:
+            raise TypeError("Cannot instantiate exception without a prefix.")
 
-    prefix = "Couldn't initialize"
+    # subclasses should set this to a descriptive prefix
+    prefix = None
 
     def format_message(self):
         if self.project_id is not None:
@@ -42,6 +32,14 @@ def format_message(self):
         return "{}: {}".format(self.prefix, self.message)
 
 
+class NotInitializedException(AnnifException):
+    """Exception raised for attempting to use a project or backend that
+    cannot be initialized, most likely since it is not yet functional
+    because of lack of vocabulary or training."""
+
+    prefix = "Couldn't initialize"
+
+
 class ConfigurationException(AnnifException):
     """Exception raised when a project or backend is misconfigured."""
 
diff --git a/tests/test_exception.py b/tests/test_exception.py
new file mode 100644
index 000000000..3fda48b5b
--- /dev/null
+++ b/tests/test_exception.py
@@ -0,0 +1,22 @@
+"""Unit tests for Annif exception classes"""
+
+import pytest
+from annif.exception import AnnifException
+from click import ClickException
+
+
+def test_annifexception_not_instantiable():
+    with pytest.raises(TypeError):
+        exc = AnnifException("test message")
+
+
+def test_annifexception_is_clickexception():
+
+    # we need to define a custom class to make an instantiable exception
+    class CustomException(AnnifException):
+        @property
+        def prefix(self):
+            return "my prefix"
+
+    exc = CustomException("test message")
+    assert isinstance(exc, ClickException)