diff --git a/src/net/cgo_unix.go b/src/net/cgo_unix.go
index 460817bdf6..a4455f45d4 100644
--- a/src/net/cgo_unix.go
+++ b/src/net/cgo_unix.go
@@ -41,18 +41,12 @@ func (eai addrinfoErrno) isAddrinfoErrno() {}
 // context is cancellable. It is intended for use with calls that don't support context
 // cancellation (cgo, syscalls). blocking func may still be running after this function finishes.
 // For the duration of the execution of the blocking function, the thread is 'acquired' using [acquireThread],
-// blocking might not be executed when the context gets cancelled.
+// blocking might not be executed when the context gets cancelled early.
 func doBlockingWithCtx[T any](ctx context.Context, lookupName string, blocking func() (T, error)) (T, error) {
-	if err := acquireThread(ctx); err != nil {
-		var zero T
-		return zero, &DNSError{
-			Name:      lookupName,
-			Err:       mapErr(ctx.Err()).Error(),
-			IsTimeout: ctx.Err() == context.DeadlineExceeded,
-		}
-	}
-
 	if ctx.Done() == nil {
+		// Context is non-cancellable, so there is no need
+		// to handle the error from acquireThread.
+		acquireThread(ctx)
 		defer releaseThread()
 		return blocking()
 	}
@@ -64,6 +58,16 @@ func doBlockingWithCtx[T any](ctx context.Context, lookupName string, blocking f
 
 	res := make(chan result, 1)
 	go func() {
+		if err := acquireThread(ctx); err != nil {
+			res <- result{
+				err: &DNSError{
+					Name:      lookupName,
+					Err:       mapErr(err).Error(),
+					IsTimeout: err == context.DeadlineExceeded,
+				},
+			}
+			return
+		}
 		defer releaseThread()
 		var r result
 		r.res, r.err = blocking()
@@ -114,7 +118,7 @@ func cgoLookupPort(ctx context.Context, network, service string) (port int, err
 		*_C_ai_family(&hints) = _C_AF_INET6
 	}
 
-	return doBlockingWithCtx(ctx, network + "/" + service, func() (int, error) {
+	return doBlockingWithCtx(ctx, network+"/"+service, func() (int, error) {
 		return cgoLookupServicePort(&hints, network, service)
 	})
 }
diff --git a/src/net/lookup_windows.go b/src/net/lookup_windows.go
index 82f90d0522..bf05aaaed9 100644
--- a/src/net/lookup_windows.go
+++ b/src/net/lookup_windows.go
@@ -55,7 +55,7 @@ func lookupProtocol(ctx context.Context, name string) (int, error) {
 	ch := make(chan result) // unbuffered
 	go func() {
 		if err := acquireThread(ctx); err != nil {
-			ch <- result{err: err}
+			ch <- result{err: mapErr(err)}
 			return
 		}
 		defer releaseThread()
@@ -115,7 +115,11 @@ func (r *Resolver) lookupIP(ctx context.Context, network, name string) ([]IPAddr
 
 	getaddr := func() ([]IPAddr, error) {
 		if err := acquireThread(ctx); err != nil {
-			return nil, err
+			return nil, &DNSError{
+				Name:      name,
+				Err:       mapErr(err).Error(),
+				IsTimeout: ctx.Err() == context.DeadlineExceeded,
+			}
 		}
 		defer releaseThread()
 		hints := syscall.AddrinfoW{
@@ -207,7 +211,11 @@ func (r *Resolver) lookupPort(ctx context.Context, network, service string) (int
 
 	// TODO(bradfitz): finish ctx plumbing. Nothing currently depends on this.
 	if err := acquireThread(ctx); err != nil {
-		return 0, err
+		return 0, &DNSError{
+			Name:      network + "/" + service,
+			Err:       mapErr(err).Error(),
+			IsTimeout: ctx.Err() == context.DeadlineExceeded,
+		}
 	}
 	defer releaseThread()
 
@@ -272,7 +280,11 @@ func (r *Resolver) lookupCNAME(ctx context.Context, name string) (string, error)
 
 	// TODO(bradfitz): finish ctx plumbing. Nothing currently depends on this.
 	if err := acquireThread(ctx); err != nil {
-		return "", err
+		return "", &DNSError{
+			Name:      name,
+			Err:       mapErr(err).Error(),
+			IsTimeout: ctx.Err() == context.DeadlineExceeded,
+		}
 	}
 	defer releaseThread()
 	var rec *syscall.DNSRecord
@@ -299,7 +311,11 @@ func (r *Resolver) lookupSRV(ctx context.Context, service, proto, name string) (
 	}
 	// TODO(bradfitz): finish ctx plumbing. Nothing currently depends on this.
 	if err := acquireThread(ctx); err != nil {
-		return "", nil, err
+		return "", nil, &DNSError{
+			Name:      name,
+			Err:       mapErr(err).Error(),
+			IsTimeout: ctx.Err() == context.DeadlineExceeded,
+		}
 	}
 	defer releaseThread()
 	var target string
@@ -331,7 +347,11 @@ func (r *Resolver) lookupMX(ctx context.Context, name string) ([]*MX, error) {
 	}
 	// TODO(bradfitz): finish ctx plumbing. Nothing currently depends on this.
 	if err := acquireThread(ctx); err != nil {
-		return nil, err
+		return nil, &DNSError{
+			Name:      name,
+			Err:       mapErr(err).Error(),
+			IsTimeout: ctx.Err() == context.DeadlineExceeded,
+		}
 	}
 	defer releaseThread()
 	var rec *syscall.DNSRecord
@@ -357,7 +377,11 @@ func (r *Resolver) lookupNS(ctx context.Context, name string) ([]*NS, error) {
 	}
 	// TODO(bradfitz): finish ctx plumbing. Nothing currently depends on this.
 	if err := acquireThread(ctx); err != nil {
-		return nil, err
+		return nil, &DNSError{
+			Name:      name,
+			Err:       mapErr(err).Error(),
+			IsTimeout: ctx.Err() == context.DeadlineExceeded,
+		}
 	}
 	defer releaseThread()
 	var rec *syscall.DNSRecord
@@ -382,7 +406,11 @@ func (r *Resolver) lookupTXT(ctx context.Context, name string) ([]string, error)
 	}
 	// TODO(bradfitz): finish ctx plumbing. Nothing currently depends on this.
 	if err := acquireThread(ctx); err != nil {
-		return nil, err
+		return nil, &DNSError{
+			Name:      name,
+			Err:       mapErr(err).Error(),
+			IsTimeout: ctx.Err() == context.DeadlineExceeded,
+		}
 	}
 	defer releaseThread()
 	var rec *syscall.DNSRecord
@@ -412,7 +440,11 @@ func (r *Resolver) lookupAddr(ctx context.Context, addr string) ([]string, error
 
 	// TODO(bradfitz): finish ctx plumbing. Nothing currently depends on this.
 	if err := acquireThread(ctx); err != nil {
-		return nil, err
+		return nil, &DNSError{
+			Name:      addr,
+			Err:       mapErr(err).Error(),
+			IsTimeout: ctx.Err() == context.DeadlineExceeded,
+		}
 	}
 	defer releaseThread()
 	arpa, err := reverseaddr(addr)
diff --git a/src/net/net.go b/src/net/net.go
index aa4335aa72..1758f15832 100644
--- a/src/net/net.go
+++ b/src/net/net.go
@@ -731,7 +731,7 @@ func acquireThread(ctx context.Context) error {
 	case threadLimit <- struct{}{}:
 		return nil
 	case <-ctx.Done():
-		return mapErr(ctx.Err())
+		return ctx.Err()
 	}
 }