diff --git a/internal/experiment/webconnectivity/cleartextflow.go b/internal/experiment/webconnectivity/cleartextflow.go
index 97b9d00..94d56be 100644
--- a/internal/experiment/webconnectivity/cleartextflow.go
+++ b/internal/experiment/webconnectivity/cleartextflow.go
@@ -233,7 +233,7 @@ func (t *CleartextFlow) httpTransaction(ctx context.Context, network, address, a
 			t.CookieJar.SetCookies(req.URL, cookies)
 		}
 		reader := io.LimitReader(resp.Body, maxbody)
-		body, err = netxlite.ReadAllContext(ctx, reader)
+		body, err = StreamAllContext(ctx, reader)
 	}
 	finished := trace.TimeSince(trace.ZeroTime)
 	t.TestKeys.AppendNetworkEvents(measurexlite.NewAnnotationArchivalNetworkEvent(
diff --git a/internal/experiment/webconnectivity/iox.go b/internal/experiment/webconnectivity/iox.go
new file mode 100644
index 0000000..b494b30
--- /dev/null
+++ b/internal/experiment/webconnectivity/iox.go
@@ -0,0 +1,79 @@
+package webconnectivity
+
+//
+// Extensions to incrementally stream-reading a response body.
+//
+
+import (
+	"context"
+	"errors"
+	"io"
+
+	"github.com/ooni/probe-cli/v3/internal/netxlite"
+)
+
+// StreamAllContext streams from the given reader [r] until
+// interrupted by [ctx] or when [r] hits the EOF.
+//
+// This function runs a background goroutine that should exit as soon
+// as [ctx] is done or when [reader] is closed, if applicable.
+//
+// This function transforms an errors.Is(err, io.EOF) to a nil error
+// such as the standard library's io.ReadAll does.
+//
+// This function might return a non-zero-length buffer along with
+// an non-nil error in the case in which we could only read a portion
+// of the body and then we were interrupted by the error.
+func StreamAllContext(ctx context.Context, reader io.Reader) ([]byte, error) {
+	// TODO(bassosimone): consider merging into the ./internal/netxlite/iox.go file
+	// once this code has been used in testing for quite some time
+	datach, errch := make(chan []byte), make(chan error)
+
+	ctx, cancel := context.WithCancel(ctx)
+	defer cancel()
+
+	go func() {
+		buffer := make([]byte, 1<<13)
+		for {
+			count, err := reader.Read(buffer)
+			if count > 0 {
+				data := buffer[:count]
+				select {
+				case datach <- data:
+					// fallthrough to check error
+				case <-ctx.Done():
+					return
+				}
+			}
+			if err != nil {
+				select {
+				case errch <- err:
+					return
+				case <-ctx.Done():
+					return
+				}
+			}
+		}
+	}()
+
+	resultbuf := make([]byte, 0, 1<<17)
+	for {
+		select {
+		case data := <-datach:
+			// TODO(bassosimone): is there a more efficient way?
+			resultbuf = append(resultbuf, data...)
+		case err := <-errch:
+			if errors.Is(err, io.EOF) {
+				// see https://github.com/ooni/probe/issues/1965
+				return resultbuf, nil
+			}
+			return resultbuf, netxlite.NewTopLevelGenericErrWrapper(err)
+		case <-ctx.Done():
+			err := ctx.Err()
+			if errors.Is(err, context.DeadlineExceeded) {
+				return resultbuf, nil
+			}
+			return resultbuf, netxlite.NewTopLevelGenericErrWrapper(err)
+		}
+	}
+}
diff --git a/internal/experiment/webconnectivity/measurer.go b/internal/experiment/webconnectivity/measurer.go
index 5da15c1..0c3406b 100644
--- a/internal/experiment/webconnectivity/measurer.go
+++ b/internal/experiment/webconnectivity/measurer.go
@@ -36,7 +36,7 @@ func (m *Measurer) ExperimentName() string {
 
 // ExperimentVersion implements model.ExperimentMeasurer.
 func (m *Measurer) ExperimentVersion() string {
-	return "0.5.13"
+	return "0.5.14"
 }
 
 // Run implements model.ExperimentMeasurer.
diff --git a/internal/experiment/webconnectivity/secureflow.go b/internal/experiment/webconnectivity/secureflow.go
index a1ab704..331a575 100644
--- a/internal/experiment/webconnectivity/secureflow.go
+++ b/internal/experiment/webconnectivity/secureflow.go
@@ -285,7 +285,7 @@ func (t *SecureFlow) httpTransaction(ctx context.Context, network, address, alpn
 			t.CookieJar.SetCookies(req.URL, cookies)
 		}
 		reader := io.LimitReader(resp.Body, maxbody)
-		body, err = netxlite.ReadAllContext(ctx, reader)
+		body, err = StreamAllContext(ctx, reader)
 	}
 	finished := trace.TimeSince(trace.ZeroTime)
 	t.TestKeys.AppendNetworkEvents(measurexlite.NewAnnotationArchivalNetworkEvent(
diff --git a/internal/netxlite/iox.go b/internal/netxlite/iox.go
index 04dde36..41b020d 100644
--- a/internal/netxlite/iox.go
+++ b/internal/netxlite/iox.go
@@ -10,6 +10,9 @@ import (
 	"io"
 )
 
+// TODO(bassosimone): consider integrating StreamAllContext from
+// internal/experiment/webconnectivity/iox.go
+
 // ReadAllContext is like io.ReadAll but reads r in a
 // background goroutine. This function will return
 // earlier if the context is cancelled. In which case