diff --git a/cmd/release/release.go b/cmd/release/release.go
index 3838068..59bb402 100644
--- a/cmd/release/release.go
+++ b/cmd/release/release.go
@@ -857,7 +857,8 @@
 }
 
 // checkRelocations runs readelf on pkg/linux_amd64/runtime/cgo.a and makes sure
-// we don't see R_X86_64_REX_GOTPCRELX. See golang.org/issue/31293.
+// we don't see R_X86_64_REX_GOTPCRELX in new Go 1.15 and Go 1.14 minor releases.
+// See golang.org/issue/31293 and golang.org/issue/40561#issuecomment-731482962.
 func (b *Build) checkRelocations(client *buildlet.Client) error {
 	if b.OS != "linux" || b.Arch != "amd64" || b.TestOnly {
 		// This check is only applicable to linux/amd64 builds.
@@ -876,11 +877,25 @@
 		return fmt.Errorf("failed to run readelf: %v", err)
 	}
 	got := out.String()
-	if strings.Contains(got, "R_X86_64_REX_GOTPCRELX") {
-		return fmt.Errorf("%s contained a R_X86_64_REX_GOTPCRELX relocation", file)
-	}
-	if !strings.Contains(got, "R_X86_64_GOTPCREL") {
-		return fmt.Errorf("%s did not contain a R_X86_64_GOTPCREL relocation; remoteErr=%v, %s", file, remoteErr, got)
+	switch {
+	default: // Go 1.16 and newer.
+		// Note: This check was kept and updated for Go 1.16, since it wasn't hard.
+		// Remove it at some point in the future if it becomes no longer useful or
+		// overly expensive to maintain.
+		if strings.Contains(got, "R_X86_64_GOTPCREL") {
+			return fmt.Errorf("%s contained a R_X86_64_GOTPCREL relocation", file)
+		}
+		if !strings.Contains(got, "R_X86_64_REX_GOTPCRELX") {
+			return fmt.Errorf("%s did not contain a R_X86_64_REX_GOTPCRELX relocation; remoteErr=%v, %s", file, remoteErr, got)
+		}
+	case strings.HasPrefix(*version, "go1.15"),
+		strings.HasPrefix(*version, "go1.14"):
+		if strings.Contains(got, "R_X86_64_REX_GOTPCRELX") {
+			return fmt.Errorf("%s contained a R_X86_64_REX_GOTPCRELX relocation", file)
+		}
+		if !strings.Contains(got, "R_X86_64_GOTPCREL") {
+			return fmt.Errorf("%s did not contain a R_X86_64_GOTPCREL relocation; remoteErr=%v, %s", file, remoteErr, got)
+		}
 	}
 	return nil
 }