diff --git a/cmd/cue/cmd/testdata/script/cmd_tags.txtar b/cmd/cue/cmd/testdata/script/cmd_tags.txtar
index e23c0bf0a..0847db19f 100644
--- a/cmd/cue/cmd/testdata/script/cmd_tags.txtar
+++ b/cmd/cue/cmd/testdata/script/cmd_tags.txtar
@@ -27,15 +27,13 @@ stderr 'no tag for "nosuchname"'
 ! exec cue cmd -t env=notadisjunct tag
 stderr '^data\.env: 2 errors in empty disjunction'
 ! exec cue cmd -t enable=notabool tag
-stderr 'invalid boolean value "notabool" for injection tag "enable"'
-# TODO: this error message seems wrong, it should say "invalid integer value"
+stderr 'invalid boolean "notabool" for injection tag "enable"'
 ! exec cue cmd -t count=notanint tag
-stderr '^data\.count: reference "notanint" not found'
-# TODO: we should reject a float when type=int with a clear error
+stderr 'invalid number for injection tag "count": illegal number start "notanint"'
 ! exec cue cmd -t count=12.34 tag
-stderr 'cannot convert incomplete value'
+stderr 'invalid int "12.34" for injection tag "count"'
 ! exec cue cmd -t toolenable=notabool tag
-stderr 'invalid boolean value "notabool" for injection tag "toolenable"'
+stderr 'invalid boolean "notabool" for injection tag "toolenable"'
 
 -- expect-stdout --
 data.json: {"env":"prod","name":"bar","enable":true,"count":5,"mult":1.5}
diff --git a/internal/cli/cli.go b/internal/cli/cli.go
index d4702e4cc..aee8a901e 100644
--- a/internal/cli/cli.go
+++ b/internal/cli/cli.go
@@ -20,7 +20,7 @@ import (
 	"cuelang.org/go/cue"
 	"cuelang.org/go/cue/ast"
 	"cuelang.org/go/cue/errors"
-	"cuelang.org/go/cue/parser"
+	"cuelang.org/go/cue/literal"
 	"cuelang.org/go/cue/token"
 )
 
@@ -28,11 +28,18 @@ func ParseValue(pos token.Pos, name, str string, k cue.Kind) (x ast.Expr, errs e
 	var expr ast.Expr
 
 	if k&cue.NumberKind != 0 {
-		var err error
-		expr, err = parser.ParseExpr(name, str)
-		if err != nil {
+		var info literal.NumInfo
+		if err := literal.ParseNum(str, &info); err != nil {
+			// Note that the wrapped err already mentions str.
 			errs = errors.Wrapf(err, pos,
 				"invalid number for injection tag %q", name)
+		} else if info.IsInt() {
+			expr = ast.NewLit(token.INT, str)
+		} else if k&cue.FloatKind == 0 {
+			errs = errors.Newf(pos,
+				"invalid int %q for injection tag %q", str, name)
+		} else {
+			expr = ast.NewLit(token.FLOAT, str)
 		}
 	}
 
@@ -41,7 +48,7 @@ func ParseValue(pos token.Pos, name, str string, k cue.Kind) (x ast.Expr, errs e
 		b, ok := boolValues[str]
 		if !ok {
 			errs = errors.Append(errs, errors.Newf(pos,
-				"invalid boolean value %q for injection tag %q", str, name))
+				"invalid boolean %q for injection tag %q", str, name))
 		} else if expr != nil || k&cue.StringKind != 0 {
 			// Convert into an expression
 			bl := ast.NewBool(b)