diff --git a/.github/workflows/go.yml b/.github/workflows/go.yml
index 809476343..e1648fcc7 100644
--- a/.github/workflows/go.yml
+++ b/.github/workflows/go.yml
@@ -105,7 +105,7 @@ jobs:
     - if: runner.os == 'Linux'
       name: Missing specification object link to definition
       run: |
-        [[ 30 -eq $(git grep -InE '^// See https:.+OpenAPI-Specification.+3[.]0[.]3[.]md#.+bject$' openapi3/*.go | grep -v _test.go | grep -v doc.go | wc -l) ]]
+        [[ 31 -eq $(git grep -InE '^// See https:.+OpenAPI-Specification.+3[.]0[.]3[.]md#.+bject$' openapi3/*.go | grep -v _test.go | grep -v doc.go | wc -l) ]]
 
     - if: runner.os == 'Linux'
       name: Style around ExtensionProps embedding
diff --git a/openapi2/openapi2.go b/openapi2/openapi2.go
index 430e39851..4927ade86 100644
--- a/openapi2/openapi2.go
+++ b/openapi2/openapi2.go
@@ -40,15 +40,13 @@ func (doc *T) UnmarshalJSON(data []byte) error {
 }
 
 func (doc *T) AddOperation(path string, method string, operation *Operation) {
-	paths := doc.Paths
-	if paths == nil {
-		paths = make(map[string]*PathItem)
-		doc.Paths = paths
+	if doc.Paths == nil {
+		doc.Paths = make(map[string]*PathItem)
 	}
-	pathItem := paths[path]
+	pathItem := doc.Paths[path]
 	if pathItem == nil {
 		pathItem = &PathItem{}
-		paths[path] = pathItem
+		doc.Paths[path] = pathItem
 	}
 	pathItem.SetOperation(method, operation)
 }
diff --git a/openapi2conv/openapi2_conv.go b/openapi2conv/openapi2_conv.go
index b81e3c2c4..989b685d5 100644
--- a/openapi2conv/openapi2_conv.go
+++ b/openapi2conv/openapi2_conv.go
@@ -1204,15 +1204,13 @@ func stripNonCustomExtensions(extensions map[string]interface{}) {
 }
 
 func addPathExtensions(doc2 *openapi2.T, path string, extensionProps openapi3.ExtensionProps) {
-	paths := doc2.Paths
-	if paths == nil {
-		paths = make(map[string]*openapi2.PathItem)
-		doc2.Paths = paths
+	if doc2.Paths == nil {
+		doc2.Paths = make(map[string]*openapi2.PathItem)
 	}
-	pathItem := paths[path]
+	pathItem := doc2.Paths[path]
 	if pathItem == nil {
 		pathItem = &openapi2.PathItem{}
-		paths[path] = pathItem
+		doc2.Paths[path] = pathItem
 	}
 	pathItem.ExtensionProps = extensionProps
 }
diff --git a/openapi3/internalize_refs.go b/openapi3/internalize_refs.go
index 6ff6b8578..dcec43b40 100644
--- a/openapi3/internalize_refs.go
+++ b/openapi3/internalize_refs.go
@@ -193,14 +193,11 @@ func (doc *T) addCallbackToSpec(c *CallbackRef, refNameResolver RefNameResolver,
 		return false
 	}
 	name := refNameResolver(c.Ref)
-	if _, ok := doc.Components.Callbacks[name]; ok {
-		c.Ref = "#/components/callbacks/" + name
-	}
 	if doc.Components.Callbacks == nil {
 		doc.Components.Callbacks = make(Callbacks)
 	}
-	doc.Components.Callbacks[name] = &CallbackRef{Value: c.Value}
 	c.Ref = "#/components/callbacks/" + name
+	doc.Components.Callbacks[name] = &CallbackRef{Value: c.Value}
 	return true
 }
 
diff --git a/openapi3/loader.go b/openapi3/loader.go
index 4cc83c0b2..ecc2ef256 100644
--- a/openapi3/loader.go
+++ b/openapi3/loader.go
@@ -281,12 +281,7 @@ func isSingleRefElement(ref string) bool {
 	return !strings.Contains(ref, "#")
 }
 
-func (loader *Loader) resolveComponent(
-	doc *T,
-	ref string,
-	path *url.URL,
-	resolved interface{},
-) (
+func (loader *Loader) resolveComponent(doc *T, ref string, path *url.URL, resolved interface{}) (
 	componentDoc *T,
 	componentPath *url.URL,
 	err error,
@@ -928,11 +923,10 @@ func (loader *Loader) resolveCallbackRef(doc *T, component *CallbackRef, documen
 					}
 					id := unescapeRefString(rest)
 
-					definitions := doc.Components.Callbacks
-					if definitions == nil {
+					if doc.Components.Callbacks == nil {
 						return failedToResolveRefFragmentPart(ref, "callbacks")
 					}
-					resolved := definitions[id]
+					resolved := doc.Components.Callbacks[id]
 					if resolved == nil {
 						return failedToResolveRefFragmentPart(ref, id)
 					}
@@ -1022,15 +1016,13 @@ func (loader *Loader) resolvePathItemRef(doc *T, entrypoint string, pathItem *Pa
 			}
 			id := unescapeRefString(rest)
 
-			definitions := doc.Paths
-			if definitions == nil {
+			if doc.Paths == nil {
 				return failedToResolveRefFragmentPart(ref, "paths")
 			}
-			resolved := definitions[id]
+			resolved := doc.Paths[id]
 			if resolved == nil {
 				return failedToResolveRefFragmentPart(ref, id)
 			}
-
 			*pathItem = *resolved
 		}
 	}
diff --git a/openapi3/openapi3.go b/openapi3/openapi3.go
index d9506a9cd..6622ef030 100644
--- a/openapi3/openapi3.go
+++ b/openapi3/openapi3.go
@@ -36,15 +36,13 @@ func (doc *T) UnmarshalJSON(data []byte) error {
 }
 
 func (doc *T) AddOperation(path string, method string, operation *Operation) {
-	paths := doc.Paths
-	if paths == nil {
-		paths = make(Paths)
-		doc.Paths = paths
+	if doc.Paths == nil {
+		doc.Paths = make(Paths)
 	}
-	pathItem := paths[path]
+	pathItem := doc.Paths[path]
 	if pathItem == nil {
 		pathItem = &PathItem{}
-		paths[path] = pathItem
+		doc.Paths[path] = pathItem
 	}
 	pathItem.SetOperation(method, operation)
 }
diff --git a/openapi3/paths.go b/openapi3/paths.go
index 2af59f2ca..0986b0557 100644
--- a/openapi3/paths.go
+++ b/openapi3/paths.go
@@ -29,8 +29,8 @@ func (paths Paths) Validate(ctx context.Context, opts ...ValidationOption) error
 		}
 
 		if pathItem == nil {
-			paths[path] = &PathItem{}
-			pathItem = paths[path]
+			pathItem = &PathItem{}
+			paths[path] = pathItem
 		}
 
 		normalizedPath, _, varsInPath := normalizeTemplatedPath(path)
@@ -109,6 +109,37 @@ func (paths Paths) Validate(ctx context.Context, opts ...ValidationOption) error
 	return nil
 }
 
+// InMatchingOrder returns paths in the order they are matched against URLs.
+// See https://github.com/OAI/OpenAPI-Specification/blob/main/versions/3.0.3.md#paths-object
+// When matching URLs, concrete (non-templated) paths would be matched
+// before their templated counterparts.
+func (paths Paths) InMatchingOrder() []string {
+	// NOTE: sorting by number of variables ASC then by descending lexicographical
+	// order seems to be a good heuristic.
+	if paths == nil {
+		return nil
+	}
+
+	vars := make(map[int][]string)
+	max := 0
+	for path := range paths {
+		count := strings.Count(path, "}")
+		vars[count] = append(vars[count], path)
+		if count > max {
+			max = count
+		}
+	}
+
+	ordered := make([]string, 0, len(paths))
+	for c := 0; c <= max; c++ {
+		if ps, ok := vars[c]; ok {
+			sort.Sort(sort.Reverse(sort.StringSlice(ps)))
+			ordered = append(ordered, ps...)
+		}
+	}
+	return ordered
+}
+
 // Find returns a path that matches the key.
 //
 // The method ignores differences in template variable names (except possible "*" suffix).
diff --git a/routers/gorillamux/router.go b/routers/gorillamux/router.go
index 6977808ed..bbf81cea8 100644
--- a/routers/gorillamux/router.go
+++ b/routers/gorillamux/router.go
@@ -56,7 +56,7 @@ func NewRouter(doc *openapi3.T) (routers.Router, error) {
 
 	muxRouter := mux.NewRouter().UseEncodedPath()
 	r := &Router{}
-	for _, path := range orderedPaths(doc.Paths) {
+	for _, path := range doc.Paths.InMatchingOrder() {
 		pathItem := doc.Paths[path]
 		if len(pathItem.Servers) > 0 {
 			if servers, err = makeServers(pathItem.Servers); err != nil {
@@ -203,31 +203,6 @@ func newSrv(serverURL string, server *openapi3.Server, varsUpdater varsf) (srv,
 	return svr, nil
 }
 
-func orderedPaths(paths map[string]*openapi3.PathItem) []string {
-	// https://github.com/OAI/OpenAPI-Specification/blob/master/versions/3.0.3.md#pathsObject
-	// When matching URLs, concrete (non-templated) paths would be matched
-	// before their templated counterparts.
-	// NOTE: sorting by number of variables ASC then by descending lexicographical
-	// order seems to be a good heuristic.
-	vars := make(map[int][]string)
-	max := 0
-	for path := range paths {
-		count := strings.Count(path, "}")
-		vars[count] = append(vars[count], path)
-		if count > max {
-			max = count
-		}
-	}
-	ordered := make([]string, 0, len(paths))
-	for c := 0; c <= max; c++ {
-		if ps, ok := vars[c]; ok {
-			sort.Sort(sort.Reverse(sort.StringSlice(ps)))
-			ordered = append(ordered, ps...)
-		}
-	}
-	return ordered
-}
-
 // Magic strings that temporarily replace "{}" so net/url.Parse() works
 var blURL, brURL = strings.Repeat("-", 50), strings.Repeat("_", 50)