diff --git a/cue/ast.go b/cue/ast.go
index 4c2dcf7..3bf6798 100644
--- a/cue/ast.go
+++ b/cue/ast.go
@@ -205,7 +205,8 @@
 		ret = obj
 
 	case *ast.Package:
-		v.walk(n.Name)
+		// NOTE: Do NOT walk the identifier of the package here, as it is not
+		// supposed to resolve to anything.
 
 	case *ast.ImportDecl:
 		for _, s := range n.Specs {
diff --git a/cue/ast_test.go b/cue/ast_test.go
index 5fa74fb..0719f1b 100644
--- a/cue/ast_test.go
+++ b/cue/ast_test.go
@@ -16,6 +16,7 @@
 
 import (
 	"bytes"
+	"strings"
 	"testing"
 
 	"cuelang.org/go/cue/errors"
@@ -381,3 +382,54 @@
 		})
 	}
 }
+
+func TestResolution(t *testing.T) {
+	testCases := []struct {
+		name string
+		in   string
+		err  string
+	}{{
+		name: "package name identifier should not resolve to anything",
+		in: `package time
+
+		import "time"
+
+		a: time.Time
+		`,
+	}, {
+		name: "duplicate_imports.cue",
+		in: `
+		import "time"
+		import time "math"
+
+		t: time.Time
+		`,
+		err: "time redeclared as imported package name",
+	}, {
+		name: "unused_import",
+		in: `
+			import "time"
+			`,
+		err: `imported and not used: "time"`,
+	}, {
+		name: "nonexisting import package",
+		in:   `import "doesnotexist"`,
+		err:  `package "doesnotexist" not found`,
+	}}
+	for _, tc := range testCases {
+		t.Run(tc.name, func(t *testing.T) {
+			var r Runtime
+			_, err := r.Compile(tc.name, tc.in)
+			got := err == nil
+			want := tc.err == ""
+			if got != want {
+				t.Fatalf("got %v; want %v", err, tc.err)
+			}
+			if err != nil {
+				if s := err.Error(); !strings.Contains(s, tc.err) {
+					t.Errorf("got %v; want %v", err, tc.err)
+				}
+			}
+		})
+	}
+}
diff --git a/cue/build.go b/cue/build.go
index c527847..356046d 100644
--- a/cue/build.go
+++ b/cue/build.go
@@ -391,6 +391,7 @@
 				"%s redeclared as imported package name\n"+
 					"\tprevious declaration at %v", name, lineStr(idx, n))
 		}
+		fields[name] = spec
 		used := false
 		for _, u := range index[name] {
 			used = true