diff --git a/canonical.go b/canonical.go
index fe69f45..eff0c38 100644
--- a/canonical.go
+++ b/canonical.go
@@ -90,10 +90,24 @@ func pcfObject(jsonMap map[string]interface{}, parentNamespace string, typeLooku
 
 	for k, v := range jsonMap {
 
-		// Reduce primitive schemas to their simple form.
-		if len(jsonMap) == 1 && k == "type" {
-			if t, ok := v.(string); ok {
-				return "\"" + t + "\"", nil
+		for k, v := range jsonMap {
+
+			if k == "type" {
+				// Reduce primitive schemas to their simple form.
+				if len(jsonMap) == 1 {
+					if t, ok := v.(string); ok {
+						return "\"" + t + "\"", nil
+					}
+				} else {
+					// Reduce logical types that annotate Avro primitive types
+					if k == "type" {
+						if _, ok := jsonMap["logicalType"]; ok {
+							if annotatedType, ok := jsonMap["type"]; ok {
+								return "\"" + annotatedType.(string) + "\"", nil
+							}
+						}
+					}
+				}
 			}
 		}
 
diff --git a/canonical_test.go b/canonical_test.go
index dd43dba..a487345 100644
--- a/canonical_test.go
+++ b/canonical_test.go
@@ -184,6 +184,20 @@ func TestCanonicalSchema(t *testing.T) {
 			Canonical: `{"name":"foo","type":"fixed","size":15}`,
 		},
 
+		// [LOGICAL TYPES] Simplify logical types that annotate primitive types
+		{
+			Schema:    `{"type":"long","logicalType":"timestamp-millis"}`,
+			Canonical: `"long"`,
+		},
+		{
+			Schema:    `{"type":"fixed", "logicalType":"custom-md5", "size":16, "name":"md5"}`,
+			Canonical: `{"name":"md5","type":"fixed","size":16}`,
+		},
+		{
+			Schema:    `{"name":"logicalRecord", "type":"record", "logicalType":"logicalRecord", "fields":[{"name":"value", "type":"long"}]}`,
+			Canonical: `{"name":"logicalRecord","type":"record","fields":[{"name":"value","type":"long"}]}`,
+		},
+
 		// [STRINGS] For all JSON string literals in the schema text, replace
 		// any escaped characters (e.g., \uXXXX escapes) with their UTF-8
 		// equivalents.