diff --git a/cmd/destroy.go b/cmd/destroy.go
index 60d5bf6d6..0bd34b724 100644
--- a/cmd/destroy.go
+++ b/cmd/destroy.go
@@ -133,7 +133,7 @@ func newDestroyCmd() *cobra.Command {
 		"Display operation as a rich diff showing the overall change")
 	cmd.PersistentFlags().IntVarP(
 		&parallel, "parallel", "p", defaultParallel,
-		"Allow P resource operations to run in parallel at once (1 for no parallelism, 0 for unbounded parallelism)")
+		"Allow P resource operations to run in parallel at once (1 for no parallelism). Defaults to unbounded.")
 	cmd.PersistentFlags().BoolVarP(
 		&refresh, "refresh", "r", false,
 		"Refresh the state of the stack's resources before this update")
diff --git a/cmd/preview.go b/cmd/preview.go
index 233d1ba46..99ea9ecd4 100644
--- a/cmd/preview.go
+++ b/cmd/preview.go
@@ -131,7 +131,7 @@ func newPreviewCmd() *cobra.Command {
 		"Display operation as a rich diff showing the overall change")
 	cmd.PersistentFlags().IntVarP(
 		&parallel, "parallel", "p", defaultParallel,
-		"Allow P resource operations to run in parallel at once (1 for no parallelism, 0 for unbounded parallelism)")
+		"Allow P resource operations to run in parallel at once (1 for no parallelism). Defaults to unbounded.")
 	cmd.PersistentFlags().BoolVar(
 		&showConfig, "show-config", false,
 		"Show configuration keys and variables")
diff --git a/cmd/refresh.go b/cmd/refresh.go
index 63f987892..bef874587 100644
--- a/cmd/refresh.go
+++ b/cmd/refresh.go
@@ -142,7 +142,7 @@ func newRefreshCmd() *cobra.Command {
 		"Display operation as a rich diff showing the overall change")
 	cmd.PersistentFlags().IntVarP(
 		&parallel, "parallel", "p", defaultParallel,
-		"Allow P resource operations to run in parallel at once (1 for no parallelism, 0 for unbounded parallelism)")
+		"Allow P resource operations to run in parallel at once (1 for no parallelism). Defaults to unbounded.")
 	cmd.PersistentFlags().BoolVar(
 		&showReplacementSteps, "show-replacement-steps", false,
 		"Show detailed resource replacement creates and deletes instead of a single step")
diff --git a/cmd/up.go b/cmd/up.go
index 56bd50ffc..aa3fbb99f 100644
--- a/cmd/up.go
+++ b/cmd/up.go
@@ -17,6 +17,7 @@ package cmd
 import (
 	"context"
 	"io/ioutil"
+	"math"
 	"os"
 
 	"github.com/pulumi/pulumi/pkg/tokens"
@@ -36,7 +37,7 @@ import (
 )
 
 const (
-	defaultParallel = 0
+	defaultParallel = math.MaxInt32
 )
 
 // nolint: vetshadow, intentionally disabling here for cleaner err declaration/assignment.
@@ -328,7 +329,7 @@ func newUpCmd() *cobra.Command {
 		"Display operation as a rich diff showing the overall change")
 	cmd.PersistentFlags().IntVarP(
 		&parallel, "parallel", "p", defaultParallel,
-		"Allow P resource operations to run in parallel at once (1 for no parallelism, 0 for unbounded parallelism)")
+		"Allow P resource operations to run in parallel at once (1 for no parallelism). Defaults to unbounded.")
 	cmd.PersistentFlags().BoolVarP(
 		&refresh, "refresh", "r", false,
 		"Refresh the state of the stack's resources before this update")
diff --git a/pkg/resource/deploy/plan.go b/pkg/resource/deploy/plan.go
index fbce7a1d1..ef3eade4c 100644
--- a/pkg/resource/deploy/plan.go
+++ b/pkg/resource/deploy/plan.go
@@ -16,6 +16,7 @@ package deploy
 
 import (
 	"context"
+	"math"
 
 	"github.com/blang/semver"
 	"github.com/pkg/errors"
@@ -50,7 +51,7 @@ func (o Options) DegreeOfParallelism() int {
 
 // InfiniteParallelism returns whether or not the requested level of parallelism is unbounded.
 func (o Options) InfiniteParallelism() bool {
-	return o.Parallel == 0
+	return o.Parallel == math.MaxInt32
 }
 
 // Events is an interface that can be used to hook interesting engine/planning events.