diff --git a/src/cmd/go/testdata/script/mod_gobuild_import.txt b/src/cmd/go/testdata/script/mod_gobuild_import.txt
index ae05250c5f..948496241e 100644
--- a/src/cmd/go/testdata/script/mod_gobuild_import.txt
+++ b/src/cmd/go/testdata/script/mod_gobuild_import.txt
@@ -2,49 +2,67 @@
 
 # go/build's Import should find modules by invoking the go command
 
-go build -o $WORK/testimport.exe ./testimport
+go build -o $WORK ./testimport ./testfindonly
 
 # GO111MODULE=off
 env GO111MODULE=off
-! exec $WORK/testimport.exe gobuild.example.com/x/y/z/w .
+! exec $WORK/testimport$GOEXE gobuild.example.com/x/y/z/w .
 
 # GO111MODULE=auto in GOPATH/src
 env GO111MODULE=auto
-exec $WORK/testimport.exe gobuild.example.com/x/y/z/w .
+exec $WORK/testimport$GOEXE gobuild.example.com/x/y/z/w .
 
 # GO111MODULE=auto outside GOPATH/src
 cd $GOPATH/other
 env GO111MODULE=auto
-exec $WORK/testimport.exe other/x/y/z/w .
+exec $WORK/testimport$GOEXE other/x/y/z/w .
 stdout w2.go
 
-! exec $WORK/testimport.exe gobuild.example.com/x/y/z/w .
+! exec $WORK/testimport$GOEXE gobuild.example.com/x/y/z/w .
 stderr 'cannot find module providing package gobuild.example.com/x/y/z/w'
 
 cd z
-exec $WORK/testimport.exe other/x/y/z/w .
+exec $WORK/testimport$GOEXE other/x/y/z/w .
 stdout w2.go
 
 # GO111MODULE=on outside GOPATH/src
 env GO111MODULE=
-exec $WORK/testimport.exe other/x/y/z/w .
+exec $WORK/testimport$GOEXE other/x/y/z/w .
 stdout w2.go
 env GO111MODULE=on
-exec $WORK/testimport.exe other/x/y/z/w .
+exec $WORK/testimport$GOEXE other/x/y/z/w .
 stdout w2.go
 
 # GO111MODULE=on in GOPATH/src
 cd $GOPATH/src
 env GO111MODULE=
-exec $WORK/testimport.exe gobuild.example.com/x/y/z/w .
+exec $WORK/testimport$GOEXE gobuild.example.com/x/y/z/w .
 stdout w1.go
 env GO111MODULE=on
-exec $WORK/testimport.exe gobuild.example.com/x/y/z/w .
+exec $WORK/testimport$GOEXE gobuild.example.com/x/y/z/w .
 stdout w1.go
 cd w
-exec $WORK/testimport.exe gobuild.example.com/x/y/z/w ..
+exec $WORK/testimport$GOEXE gobuild.example.com/x/y/z/w ..
 stdout w1.go
 
+# go/build's Import in FindOnly mode should find directories by invoking the go command
+#
+# Calling build.Import in build.FindOnly mode on an import path of a Go package
+# that produces errors when loading (e.g., due to build constraints not matching
+# the current build context) should return the package directory and nil error.
+
+# Issue 31603: Import with non-empty srcDir should work.
+env GO111MODULE=on
+exec $WORK/testfindonly$GOEXE gobuild.example.com/x/y/z/i $WORK
+! stdout 'build constraints'
+stdout '^dir=\$WORK.+i err=<nil>$'
+
+# Issue 37153: Import with empty srcDir should work.
+env GO111MODULE=on
+exec $WORK/testfindonly$GOEXE gobuild.example.com/x/y/z/i ''
+! stdout 'build constraints'
+stdout '^dir=\$WORK.+i err=<nil>$'
+
 -- go.mod --
 module gobuild.example.com/x/y/z
 
@@ -54,6 +72,11 @@ package z
 -- w/w1.go --
 package w
 
+-- i/i.go --
+// +build i
+
+package i
+
 -- testimport/x.go --
 package main
 
@@ -89,6 +112,20 @@ func main() {
 	fmt.Printf("%s\n%s\n", p1.Dir, strings.Join(p1.GoFiles, " "))
 }
 
+-- testfindonly/x.go --
+package main
+
+import (
+	"fmt"
+	"go/build"
+	"os"
+)
+
+func main() {
+	p, err := build.Import(os.Args[1], os.Args[2], build.FindOnly)
+	fmt.Printf("dir=%s err=%v\n", p.Dir, err)
+}
+
 -- $GOPATH/other/go.mod --
 module other/x/y
 
diff --git a/src/go/build/build.go b/src/go/build/build.go
index e89aa7708d..1a122c615f 100644
--- a/src/go/build/build.go
+++ b/src/go/build/build.go
@@ -1015,8 +1015,6 @@ var errNoModules = errors.New("not using modules")
 // Then we reinvoke it for every dependency. But this is still better than not working at all.
 // See golang.org/issue/26504.
 func (ctxt *Context) importGo(p *Package, path, srcDir string, mode ImportMode) error {
-	const debugImportGo = false
-
 	// To invoke the go command,
 	// we must not being doing special things like AllowBinary or IgnoreVendor,
 	// and all the file system callbacks must be nil (we're meant to use the local file system).
@@ -1135,15 +1133,15 @@ func (ctxt *Context) importGo(p *Package, path, srcDir string, mode ImportMode)
 	}
 	dir := f[0]
 	errStr := strings.TrimSpace(f[4])
-	if errStr != "" && p.Dir == "" {
-		// If 'go list' could not locate the package, return the same error that
-		// 'go list' reported.
-		// If 'go list' did locate the package (p.Dir is not empty), ignore the
-		// error. It was probably related to loading source files, and we'll
-		// encounter it ourselves shortly.
+	if errStr != "" && dir == "" {
+		// If 'go list' could not locate the package (dir is empty),
+		// return the same error that 'go list' reported.
 		return errors.New(errStr)
 	}
 
+	// If 'go list' did locate the package, ignore the error.
+	// It was probably related to loading source files, and we'll
+	// encounter it ourselves shortly if the FindOnly flag isn't set.
 	p.Dir = dir
 	p.ImportPath = f[1]
 	p.Root = f[2]