diff --git a/src/cmd/go/internal/modcmd/download.go b/src/cmd/go/internal/modcmd/download.go
index 42b06dbc95..0e5af85237 100644
--- a/src/cmd/go/internal/modcmd/download.go
+++ b/src/cmd/go/internal/modcmd/download.go
@@ -138,14 +138,14 @@ func runDownload(ctx context.Context, cmd *base.Command, args []string) {
 	sem := make(chan token, runtime.GOMAXPROCS(0))
 	infos, infosErr := modload.ListModules(ctx, args, 0)
 	if !haveExplicitArgs {
-		// 'go mod download' is sometimes run without arguments to pre-populate
-		// the module cache. It may fetch modules that aren't needed to build
-		// packages in the main mdoule. This is usually not intended, so don't save
-		// sums for downloaded modules (golang.org/issue/45332).
-		// TODO(golang.org/issue/45551): For now, save sums needed to load the
-		// build list (same as 1.15 behavior). In the future, report an error if
-		// go.mod or go.sum need to be updated after loading the build list.
-		modload.WriteGoMod(ctx)
+		// 'go mod download' is sometimes run without arguments to pre-populate the
+		// module cache. It may fetch modules that aren't needed to build packages
+		// in the main mdoule. This is usually not intended, so don't save sums for
+		// downloaded modules (golang.org/issue/45332).
+		// TODO(golang.org/issue/45551): For now, in ListModules, save sums needed
+		// to load the build list (same as 1.15 behavior). In the future, report an
+		// error if go.mod or go.sum need to be updated after loading the build
+		// list.
 		modload.DisallowWriteGoMod()
 	}
 
diff --git a/src/cmd/go/internal/modload/init.go b/src/cmd/go/internal/modload/init.go
index 86c0db3fe4..ea404b9f78 100644
--- a/src/cmd/go/internal/modload/init.go
+++ b/src/cmd/go/internal/modload/init.go
@@ -1122,12 +1122,11 @@ func keepSums(ctx context.Context, ld *loader, rs *Requirements, which whichSums
 		}
 	}
 
-	if rs.depth == lazy && rs.graph.Load() == nil {
-		// The main module is lazy and we haven't needed to load the module graph so
-		// far. Don't incur the cost of loading it now — since we haven't loaded the
-		// graph, we probably don't have any checksums to contribute to the distant
-		// parts of the graph anyway. Instead, just request sums for the roots that
-		// we know about.
+	if rs.graph.Load() == nil {
+		// The module graph was not loaded, possibly because the main module is lazy
+		// or possibly because we haven't needed to load the graph yet.
+		// Save sums for the root modules (or their replacements), but don't
+		// incur the cost of loading the graph just to find and retain the sums.
 		for _, m := range rs.rootModules {
 			r := resolveReplacement(m)
 			keep[modkey(r)] = true
diff --git a/src/cmd/go/testdata/script/mod_download.txt b/src/cmd/go/testdata/script/mod_download.txt
index ad640b45de..c2b72b2a02 100644
--- a/src/cmd/go/testdata/script/mod_download.txt
+++ b/src/cmd/go/testdata/script/mod_download.txt
@@ -167,5 +167,4 @@ require (
 -- update/go.sum.update --
 golang.org/x/text v0.0.0-20170915032832-14c0d48ead0c/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
 rsc.io/quote v1.5.2/go.mod h1:LzX7hefJvL54yjefDEDHNONDjII0t9xZLPXsUe+TKr0=
-rsc.io/sampler v1.2.1/go.mod h1:T1hPZKmBbMNahiBKFy5HrXp6adAjACjK9JXDnKaTXpA=
 rsc.io/sampler v1.3.0/go.mod h1:T1hPZKmBbMNahiBKFy5HrXp6adAjACjK9JXDnKaTXpA=