diff --git a/include/sound/hda_codec.h b/include/sound/hda_codec.h
index 1d05f991f2ce7e..b95b59c4e7887c 100644
--- a/include/sound/hda_codec.h
+++ b/include/sound/hda_codec.h
@@ -260,6 +260,9 @@ struct hda_codec {
 	unsigned int no_stream_clean_at_suspend:1; /* do not clean streams at suspend */
 	unsigned int ctl_dev_id:1; /* old control element id build behaviour */
 	unsigned int eld_jack_detect:1;	/* Machine jack-detection by ELD */
+	unsigned int constrain_pcms:1;	/* narrow the PCMs with hw_constraints
+					 * because runtime->hw is not honoured
+					 */
 
 	unsigned long power_on_acct;
 	unsigned long power_off_acct;
diff --git a/sound/hda/codecs/hdmi/hdmi.c b/sound/hda/codecs/hdmi/hdmi.c
index 1e7a05c8773311..da26eb51d232d4 100644
--- a/sound/hda/codecs/hdmi/hdmi.c
+++ b/sound/hda/codecs/hdmi/hdmi.c
@@ -830,6 +830,32 @@ static void pin_cvt_fixup(struct hda_codec *codec,
 		spec->ops.pin_cvt_fixup(codec, per_pin, cvt_nid);
 }
 
+/*
+ * Repeat the narrowing of the PCM as hw_constraints for a codec which asked for
+ * it. The runtime->hw of such a codec is overwritten after this open returns,
+ * losing everything set there, while nothing touches the constraints. A DSP
+ * driver exposing the PCM as an ASoC dynamic PCM backend is the case that needs
+ * it, the frontend being what userspace negotiates against there.
+ */
+static void hdmi_pcm_add_constraints(struct hda_pcm_stream *hinfo,
+				     struct snd_pcm_substream *substream,
+				     struct hdmi_eld *eld)
+{
+	snd_pcm_hw_constraint_mask64(substream->runtime,
+				     SNDRV_PCM_HW_PARAM_FORMAT, hinfo->formats);
+	snd_pcm_hw_constraint_minmax(substream->runtime,
+				     SNDRV_PCM_HW_PARAM_CHANNELS,
+				     hinfo->channels_min, hinfo->channels_max);
+	/*
+	 * The rates a converter supports are a mask, which no constraint can
+	 * take, so they are left to the caps the PCM was created with. The ELD
+	 * rates are a finer restriction than @hinfo can express anyway, being
+	 * correlated with the channel count.
+	 */
+	if (eld)
+		snd_pcm_hw_constraint_eld(substream->runtime, eld->eld_buffer);
+}
+
 /* called in hdmi_pcm_open when no pin is assigned to the PCM */
 static int hdmi_pcm_open_no_pin(struct hda_pcm_stream *hinfo,
 			 struct hda_codec *codec,
@@ -871,6 +897,9 @@ static int hdmi_pcm_open_no_pin(struct hda_pcm_stream *hinfo,
 	runtime->hw.formats = hinfo->formats;
 	runtime->hw.rates = hinfo->rates;
 
+	if (codec->constrain_pcms)
+		hdmi_pcm_add_constraints(hinfo, substream, NULL);
+
 	snd_pcm_hw_constraint_step(substream->runtime, 0,
 				   SNDRV_PCM_HW_PARAM_CHANNELS, 2);
 	return 0;
@@ -957,6 +986,12 @@ static int hdmi_pcm_open(struct hda_pcm_stream *hinfo,
 	runtime->hw.formats = hinfo->formats;
 	runtime->hw.rates = hinfo->rates;
 
+	if (codec->constrain_pcms) {
+		if (static_hdmi_pcm || !eld->eld_valid)
+			eld = NULL;
+		hdmi_pcm_add_constraints(hinfo, substream, eld);
+	}
+
 	snd_pcm_hw_constraint_step(substream->runtime, 0,
 				   SNDRV_PCM_HW_PARAM_CHANNELS, 2);
 	return 0;
diff --git a/sound/soc/sof/intel/hda-codec.c b/sound/soc/sof/intel/hda-codec.c
index fd371850b0d691..b972142a25c197 100644
--- a/sound/soc/sof/intel/hda-codec.c
+++ b/sound/soc/sof/intel/hda-codec.c
@@ -181,6 +181,15 @@ static int hda_codec_probe(struct snd_sof_dev *sdev, int address)
 	hda_priv->dev_index = address;
 	dev_set_drvdata(&codec->core.dev, hda_priv);
 
+	/*
+	 * Every codec here is exposed as a dynamic PCM backend, and the ASoC
+	 * core overwrites the runtime->hw of those with what topology says,
+	 * after the codec has set it up. Ask for hw_constraints instead, which
+	 * survive, so that a restriction only the codec knows about reaches the
+	 * frontend that userspace negotiates against.
+	 */
+	codec->constrain_pcms = 1;
+
 	if ((resp & 0xFFFF0000) == IDISP_VID_INTEL) {
 		if (!hbus->core.audio_component) {
 			dev_dbg(sdev->dev,