diff --git a/github/github.go b/github/github.go
index f0c0d5abf91..5566fc16691 100644
--- a/github/github.go
+++ b/github/github.go
@@ -159,7 +159,7 @@ var errNonNilContext = errors.New("context must be non-nil")
 
 // A Client manages communication with the GitHub API.
 type Client struct {
-	clientMu              sync.Mutex   // clientMu protects the client during calls that modify the CheckRedirect func.
+	clientMu              sync.Mutex   // clientMu protects the client fields during copy and Client calls.
 	client                *http.Client // HTTP client used to communicate with the API.
 	clientIgnoreRedirects *http.Client // HTTP client used to communicate with the API on endpoints where we don't want to follow redirects.
 
diff --git a/github/migrations.go b/github/migrations.go
index e53a9ca9398..3e9f92b1b10 100644
--- a/github/migrations.go
+++ b/github/migrations.go
@@ -9,8 +9,6 @@ import (
 	"context"
 	"errors"
 	"fmt"
-	"net/http"
-	"strings"
 )
 
 // MigrationService provides access to the migration related functions
@@ -186,29 +184,18 @@ func (s *MigrationService) MigrationArchiveURL(ctx context.Context, org string,
 	if err != nil {
 		return "", err
 	}
-
 	req.Header.Set("Accept", mediaTypeMigrationsPreview)
 
-	s.client.clientMu.Lock()
-	defer s.client.clientMu.Unlock()
-
-	// Disable the redirect mechanism because AWS fails if the GitHub auth token is provided.
-	var loc string
-	saveRedirect := s.client.client.CheckRedirect
-	s.client.client.CheckRedirect = func(req *http.Request, _ []*http.Request) error {
-		loc = req.URL.String()
-		return errors.New("disable redirect")
+	loc, _, err := s.client.bareDoUntilFound(ctx, req, 10)
+	if err != nil {
+		return "", err
 	}
-	defer func() { s.client.client.CheckRedirect = saveRedirect }()
 
-	_, err = s.client.Do(ctx, req, nil) // expect error from disable redirect
-	if err == nil {
+	if loc == nil {
 		return "", errors.New("expected redirect, none provided")
 	}
-	if !strings.Contains(err.Error(), "disable redirect") {
-		return "", err
-	}
-	return loc, nil
+
+	return loc.String(), nil
 }
 
 // DeleteMigration deletes a previous migration archive.
diff --git a/github/migrations_test.go b/github/migrations_test.go
index 68ef325ff8b..002acdc48f6 100644
--- a/github/migrations_test.go
+++ b/github/migrations_test.go
@@ -128,7 +128,7 @@ func TestMigrationService_MigrationStatus(t *testing.T) {
 	})
 }
 
-func TestMigrationService_MigrationArchiveURL(t *testing.T) {
+func TestMigrationService_MigrationArchiveURL_Redirect(t *testing.T) {
 	t.Parallel()
 	client, mux, _ := setup(t)
 
@@ -161,6 +161,28 @@ func TestMigrationService_MigrationArchiveURL(t *testing.T) {
 	})
 }
 
+func TestMigrationService_MigrationArchiveURL_NoRedirect(t *testing.T) {
+	t.Parallel()
+	client, mux, _ := setup(t)
+
+	mux.HandleFunc("/orgs/o/migrations/1/archive", func(w http.ResponseWriter, r *http.Request) {
+		testMethod(t, r, "GET")
+		testHeader(t, r, "Accept", mediaTypeMigrationsPreview)
+
+		w.WriteHeader(http.StatusOK)
+		assertWrite(t, w, []byte("0123456789abcdef"))
+	})
+
+	ctx := t.Context()
+	got, err := client.Migrations.MigrationArchiveURL(ctx, "o", 1)
+	if err == nil {
+		t.Error("Migrations.MigrationArchiveURL did not return expected error")
+	}
+	if got != "" {
+		t.Errorf("MigrationArchiveURL = %+v, want %+v", got, "")
+	}
+}
+
 func TestMigrationService_DeleteMigration(t *testing.T) {
 	t.Parallel()
 	client, mux, _ := setup(t)
diff --git a/github/repos_releases.go b/github/repos_releases.go
index 18bbe885a53..a0876cf38ce 100644
--- a/github/repos_releases.go
+++ b/github/repos_releases.go
@@ -365,36 +365,27 @@ func (s *RepositoriesService) DownloadReleaseAsset(ctx context.Context, owner, r
 	}
 	req.Header.Set("Accept", defaultMediaType)
 
-	s.client.clientMu.Lock()
-	defer s.client.clientMu.Unlock()
-
-	var loc string
-	saveRedirect := s.client.client.CheckRedirect
-	s.client.client.CheckRedirect = func(req *http.Request, _ []*http.Request) error {
-		loc = req.URL.String()
-		return errors.New("disable redirect")
+	loc, resp, err := s.client.bareDoUntilFound(ctx, req, 10)
+	if err != nil {
+		return nil, "", err
 	}
-	defer func() { s.client.client.CheckRedirect = saveRedirect }()
 
-	req = withContext(ctx, req)
-	resp, err := s.client.client.Do(req)
-	if err != nil {
-		if !strings.Contains(err.Error(), "disable redirect") {
-			return nil, "", err
-		}
-		if followRedirectsClient != nil {
-			rc, err := s.downloadReleaseAssetFromURL(ctx, followRedirectsClient, loc)
-			return rc, "", err
-		}
-		return nil, loc, nil // Intentionally return no error with valid redirect URL.
+	// No redirect, stream the response body directly.
+	if loc == nil {
+		return resp.Body, "", nil
 	}
 
-	if err := CheckResponse(resp); err != nil {
-		_ = resp.Body.Close()
-		return nil, "", err
+	// Close body as it's not needed when following redirects or returning the redirect URL.
+	_ = resp.Body.Close()
+
+	// Got a redirect URL.
+	redirectStr := loc.String()
+	if followRedirectsClient != nil {
+		rc, err := s.downloadReleaseAssetFromURL(ctx, followRedirectsClient, redirectStr)
+		return rc, "", err
 	}
 
-	return resp.Body, "", nil
+	return nil, redirectStr, nil
 }
 
 func (s *RepositoriesService) downloadReleaseAssetFromURL(ctx context.Context, followRedirectsClient *http.Client, url string) (rc io.ReadCloser, err error) {