diff --git a/cli/azd/pkg/azapi/stack_deployments.go b/cli/azd/pkg/azapi/stack_deployments.go
index f410d83a255..c9197d6b2ac 100644
--- a/cli/azd/pkg/azapi/stack_deployments.go
+++ b/cli/azd/pkg/azapi/stack_deployments.go
@@ -125,7 +125,10 @@ func (d *StackDeployments) GetSubscriptionDeployment(
 
 	err = retry.Do(
 		ctx,
-		retry.WithMaxDuration(10*time.Minute, retry.NewConstant(5*time.Second)),
+		retry.WithMaxDuration(
+			10*time.Minute,
+			retry.WithCappedDuration(10*time.Second, retry.NewExponential(1*time.Second)),
+		),
 		func(ctx context.Context) error {
 			response, err := client.GetAtSubscription(ctx, deploymentName, nil)
 			if err != nil {
@@ -201,7 +204,10 @@ func (d *StackDeployments) GetResourceGroupDeployment(
 
 	err = retry.Do(
 		ctx,
-		retry.WithMaxDuration(10*time.Minute, retry.NewConstant(5*time.Second)),
+		retry.WithMaxDuration(
+			10*time.Minute,
+			retry.WithCappedDuration(10*time.Second, retry.NewExponential(1*time.Second)),
+		),
 		func(ctx context.Context) error {
 			response, err := client.GetAtResourceGroup(ctx, resourceGroupName, deploymentName, nil)
 			if err != nil {
diff --git a/cli/azd/pkg/azsdk/funcapp_host_client.go b/cli/azd/pkg/azsdk/funcapp_host_client.go
index d7b3431747d..89622229b74 100644
--- a/cli/azd/pkg/azsdk/funcapp_host_client.go
+++ b/cli/azd/pkg/azsdk/funcapp_host_client.go
@@ -138,8 +138,13 @@ func (c *FuncAppHostClient) waitForDeployment(ctx context.Context, location stri
 		}
 
 		if deploymentNotFoundAttempts <= 3 && response.StatusCode == http.StatusNotFound {
+			response.Body.Close()
 			deploymentNotFoundAttempts++
-			time.Sleep(pollDelay)
+			select {
+			case <-ctx.Done():
+				return PublishResponse{}, ctx.Err()
+			case <-time.After(pollDelay):
+			}
 			continue
 		}
 
@@ -149,19 +154,24 @@ func (c *FuncAppHostClient) waitForDeployment(ctx context.Context, location stri
 		// This 404 is due to the deployment worker being "recycled".
 		// This shortcoming would be fixed by work item https://msazure.visualstudio.com/Antares/_workitems/edit/24715654.
 		if response.StatusCode == http.StatusNotFound && lastResponse != nil {
+			response.Body.Close()
 			return *lastResponse, nil
 		}
 
 		if response.StatusCode != http.StatusAccepted && response.StatusCode != http.StatusOK {
-			return PublishResponse{}, runtime.NewResponseError(response)
+			err := runtime.NewResponseError(response)
+			response.Body.Close()
+			return PublishResponse{}, err
 		}
 
 		// Server always returns status code of OK-200 whether the deployment is in-progress or complete.
 		// Thus, we always read the response body to determine the actual status.
 		resp := PublishResponse{}
 		if err := runtime.UnmarshalAsJSON(response, &resp); err != nil {
+			response.Body.Close()
 			return PublishResponse{}, err
 		}
+		response.Body.Close()
 
 		switch resp.Status {
 		case PublishStatusCancelled:
@@ -181,7 +191,7 @@ func (c *FuncAppHostClient) waitForDeployment(ctx context.Context, location stri
 
 		delay := pollDelay
 		if retryAfter := httputil.RetryAfter(response); retryAfter > 0 {
-			delay = pollDelay
+			delay = retryAfter
 		}
 
 		select {
diff --git a/cli/azd/pkg/project/service_target_staticwebapp.go b/cli/azd/pkg/project/service_target_staticwebapp.go
index ec3167cdd44..291f3124a42 100644
--- a/cli/azd/pkg/project/service_target_staticwebapp.go
+++ b/cli/azd/pkg/project/service_target_staticwebapp.go
@@ -290,7 +290,11 @@ func (at *staticWebAppTarget) verifyDeployment(ctx context.Context, targetResour
 			return fmt.Errorf("failed verifying static web app deployment. Still in %s state", envProps.Status)
 		}
 
-		time.Sleep(5 * time.Second)
+		select {
+		case <-ctx.Done():
+			return ctx.Err()
+		case <-time.After(5 * time.Second):
+		}
 	}
 
 	return nil